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Academic Journal

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Relation: mr:MR3619989; zbl:Zbl 06738572; reference:[1] Albertson, M.: Open Problem 2.The Theory and Applications of Graphs. Proc. 4th Int. Conf., Kalamazoo, 1980 (1981), John Wiley & Sons, New York. Zbl 0459.00006, MR 0634511; reference:[2] Alon, N., Ding, G., Oporowski, B., Vertigan, D.: Partitioning into graphs with only small components.J. Comb. Theory, Ser. B 87 (2003), 231-243. Zbl 1023.05045, MR 1957474, 10.1016/S0095-8956(02)00006-0; reference:[3] Berke, R.: Coloring and Transversals of Graphs. Ph.D. thesis.ETH, Zurich (2008).; reference:[4] Boesch, F., Tindell, R.: Circulants and their connectivities.J. Graph Theory 8 (1984), 487-499. Zbl 0549.05048, MR 0766498, 10.1002/jgt.3190080406; reference:[5] Burr, S. A.: Diagonal Ramsey numbers for small graphs.J. Graph Theory 7 (1983), 57-69. Zbl 0513.05041, MR 0693021, 10.1002/jgt.3190070108; reference:[6] Burr, S. A., Erdős, P., Faudree, R. J., Schelp, R. H.: On the difference between consecutive Ramsey numbers.Util. Math. 35 (1989), 115-118. Zbl 0678.05039, MR 0992396; reference:[7] Chappell, G. G.: GraphR [computer software]. August 26, 2016.Available at https://www.cs.uaf.edu/users/chappell/public_html/papers/graphr/.; reference:[8] Chappell, G. G., Gimbel, J.: On defective Ramsey numbers.Avaible at https://www.cs.uaf.edu/users/chappell/public_html/papers/defram/.; reference:[9] Chartrand, G., Lesniak, L., Zhang, P.: Graphs & Digraphs.CRC Press, Boca Raton (2011). Zbl 1211.05001, MR 2766107; reference:[10] Cockayne, E. J., Mynhardt, C. M.: On 1-dependent Ramsey numbers for graphs.Discuss. Math., Graph Theory 19 (1999), 93-110. Zbl 0932.05061, MR 1704453, 10.7151/dmgt.1088; reference:[11] Cowen, L. J., Cowen, R. H., Woodall, D. R.: Defective colorings of graphs in surfaces: partitions into subgraphs of bounded valency.J. Graph Theory 10 (1986), 187-195. Zbl 0596.05024, MR 0890224, 10.1002/jgt.3190100207; reference:[12] Cowen, L., Goddard, W., Jesurum, C. E.: Defective coloring revisited.J. Graph Theory 24 (1997), 205-219. Zbl 0877.05019, MR 1431666, 10.1002/(SICI)1097-0118(199703)24; reference:[13] Eaton, N., Hull, T.: Defective list colorings of planar graphs.Bull. Inst. Combin. Appl. 25 (1999), 79-87. Zbl 0916.05026, MR 1668108; reference:[14] Ekim, T., Gimbel, J.: Some defective parameters in graphs.Graphs Combin. 29 (2013), 213-224. Zbl 1263.05028, MR 3027597, 10.1007/s00373-011-1111-5; reference:[15] Era, H., Urabe, M.: On the $k$-independent sets of graphs.Proc. Fac. Sci. Tokai Univ. 26 (1991), 1-4. Zbl 0752.05032, MR 1148560; reference:[16] Erdős, P.: Some remarks on the theory of graphs.Bull. Am. Math. Soc. 53 (1947), 292-294. Zbl 0032.19203, MR 0019911, 10.1090/S0002-9904-1947-08785-1; reference:[17] Erdős, P., Szekeres, G.: A combinatorial problem in geometry.Compos. Math. 2 (1935), 463-470. Zbl 0012.27010, MR 1556929; reference:[18] Esperet, L., Joret, G.: Colouring planar graphs with three colours and no large monochromatic components.Comb. Probab. Comput. 23 (2014), 551-570. Zbl 06325560, MR 3217360, 10.1017/S0963548314000170; reference:[19] Esperet, L., Ochem, P.: Islands in graphs on surfaces.SIAM J. Discrete Math. 30 (2016), 206-219. Zbl 1329.05105, MR 3455135, 10.1137/140957883; reference:[20] Farrugia, A.: Vertex-partitioning into fixed additive induced-hereditary properties is NP-hard.Electron. J. Comb. 11 (2004), research paper R46, 9 pages. Zbl 1053.05046, MR 2097312; reference:[21] Fink, J. F., Jacobson, M. S.: On $n$-domination, $n$-dependence and forbidden subgraphs.Graph Theory with Applications to Algorithms and Computer Science. Proc. 5th Quadr. Int. Conf. on the Theory and Applications of Graphs with special emphasis on Algorithms and Computer Science Applications, Kalamazoo, 1984 (Y. Alavi et al., eds.) Wiley-Interscience Publication, John Wiley & Sons, New York (1985), 301-311. Zbl 0573.05050, MR 0812672; reference:[22] Garey, M. R., Johnson, D. S.: The rectilinear Steiner tree problem is NP-complete.SIAM J. Appl. Math. 32 (1977), 826-834. Zbl 0396.05009, MR 0443426, 10.1137/0132071; reference:[23] Garey, M. R., Johnson, D. S., Stockmeyer, L.: Some simplified NP-complete graph problems.Theor. Comput. Sci. 1 (1976), 237-267. Zbl 0338.05120, MR 0411240, 10.1016/0304-3975(76)90059-1; reference:[24] Gimbel, J., Hartman, C.: Subcolorings and the subchromatic number of a graph.Discrete Math. 272 (2003), 139-154. Zbl 1028.05032, MR 2009539, 10.1016/S0012-365X(03)00177-8; reference:[25] Grötzsch, H.: Ein Dreifarbensatz für dreikreisfreie Netze auf der Kugel.Wiss. Z. Martin-Luther-Univ. Halle-Wittenberg, Math.-Natur. Reihe 8 (1959), 109-120. Zbl 0089.39506, MR 0116320; reference:[26] Haxell, P., Szabó, T., Tardos, G.: Bounded size components - partitions and transversals.J. Comb. Theory, Ser. B 88 (2003), 281-297. Zbl 1033.05083, MR 1983359, 10.1016/S0095-8956(03)00031-5; reference:[27] Kleinberg, J., Motwani, R., Raghavan, P., Venkatasubramanian, S.: Storage management for evolving databases.Proc. 38th IEEE Symposium on Foundations of Computer Science (FOCS 97) (1997), 353-362.; reference:[28] Linial, N., Matoušek, J., Sheffet, O., Tardos, G.: Graph colouring with no large monochromatic components.Comb. Probab. Comput. 17 (2008), 577-589. Zbl 1171.05021, MR 2433942, 10.1017/S0963548308009140; reference:[29] Lortz, R., Mengersen, I.: Bounds on Ramsey numbers of certain complete bipartite graphs.Result. Math. 41 (2002), 140-149. Zbl 1009.05100, MR 1888725, 10.1007/BF03322761; reference:[30] Lovász, L.: On decomposition of graphs.Stud. Sci. Math. Hung. 1 (1966), 237-238. Zbl 0151.33401, MR 0202630; reference:[31] Matoušek, J., Přívětivý, A.: Large monochromatic components in two-colored grids.SIAM J. Discrete Math. 22 (2008), 295-311. Zbl 1159.05021, MR 2383243, 10.1137/070684112; reference:[32] Nešetřil, J., Rapaud, A., Sopena, E.: Colorings and girth of oriented planar graphs.Discrete Math. 165/166 (1997), 519-530. Zbl 0873.05042, MR 1439297, 10.1016/S0012-365X(96)00198-7; reference:[33] Radziszowski, S. P.: Small Ramsey numbers. Revision \# 14: January 12, 2014.Electron. J. Comb. DS1, Dynamic Surveys (electronic only) (1996), 94 pages. Zbl 0953.05048, MR 1670625; reference:[34] Thomassen, C.: Five-coloring maps on surfaces.J. Comb. Theory, Ser. B 59 (1993), 89-105. Zbl 0794.05026, MR 1234386, 10.1006/jctb.1993.1057; reference:[35] Thomassen, C.: A short list color proof of Grötzsch's theorem.J. Comb. Theory, Ser. B 88 (2003), 189-192. Zbl 1025.05022, MR 1974149, 10.1016/S0095-8956(03)00029-7

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Academic Journal

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Relation: mr:MR2741880; zbl:Zbl 1224.05164; reference:[1] Allouche J.-P., Shallit J.: Automatic Sequences: Theory, Applications, Generalizations.Cambridge University Press, Cambridge, 2003. Zbl 1086.11015, MR 1997038; reference:[2] Alon N., Grytczuk J., Hałuszczak M., Riordan O.: Nonrepetitive colorings of graphs.Random Structures Algorithms 21 (2002), no. 3–4, 336–346. MR 1945373, 10.1002/rsa.10057; reference:[3] Alon N., Smorodinsky S.: Conflict-free colorings of shallow discs.Internat. J. Comput. Geom. Appl. 18 (2008), no. 6, 599–604. Zbl 1184.05038, MR 2479564, 10.1142/S0218195908002775; reference:[4] Bar-Noy A., Cheilaris P., Lampis M., Mitsou V., Zachos S.: Ordered coloring grids and related graphs.Proceedings of the 16th International Colloquium on Structural Information and Communication Complexity (SIROCCO), 2009, pp. 30–43. MR 2671334; reference:[5] Bar-Noy A., Cheilaris P., Smorodinsky S.: Deterministic conflict-free coloring for intervals: from offline to online.ACM Trans. Algorithms 4 (2008), no. 4, 18pp. MR 2446963, 10.1145/1383369.1383375; reference:[6] Cheilaris P.: Conflict-free coloring.Ph.D. thesis, City University of New York, 2009.; reference:[7] Chen K., Fiat A., Kaplan H., Levy M., Matoušek J., Mossel E., Pach J., Sharir M., Smorodinsky S., Wagner U., Welzl E.: Online conflict-free coloring for intervals.SIAM J. Comput. 36 (2007), no. 5, 1342–1359. MR 2284084, 10.1137/S0097539704446682; reference:[8] Currie J.D.: There are ternary circular square-free words of length $n$ for $n \geq 18$.Electron. J. Combin. 9 (2002), no. 1, N10. Zbl 1057.68081, MR 1936865; reference:[9] Djidjev H.N.: On the problem of partitioning planar graphs.SIAM J. Algebraic Discrete Methods 3 (1982), 229–240. Zbl 0503.05057, MR 0655563, 10.1137/0603022; reference:[10] Erlebach T., Pagourtzis A., Potika K., Stefanakos S.: Resource allocation problems in multifiber WDMtree networks.Proceedings of 29th Workshop on Graph Theoretic Concepts in Computer Science (WG 2003), Lecture Notes in Comput. Sci., 2880, Berlin, 2003, pp. 218–229. MR 2080082; reference:[11] Even G., Lotker Z., Ron D., Smorodinsky S.: Conflict-free colorings of simple geometric regions with applications to frequency assignment in cellular networks.SIAM J. Comput. 33 (2003), 94–136. Zbl 1069.68120, MR 2033655, 10.1137/S0097539702431840; reference:[12] Grytczuk J.: Nonrepetitive graph coloring.Graph Theory, Trends in Mathematics, Birkhäuser, Basel, 2007, pp. 209–218. Zbl 1120.05029, MR 2279177; reference:[13] Har-Peled S., Smorodinsky S.: Conflict-free coloring of points and simple regions in the plane.Discrete Comput. Geom. 34 (2005), 47–70. Zbl 1066.05064, MR 2140882, 10.1007/s00454-005-1162-6; reference:[14] Iyer A.V., Ratliff H.R., Vijayan G.: Optimal node ranking of trees.Inform. Process. Lett. 28 (1988), 225–229. Zbl 0661.68063, MR 0958825, 10.1016/0020-0190(88)90194-9; reference:[15] Jordan C.: Sur les assemblages de lignes.J. Reine Angew. Math. 70 (1869), 185–190.; reference:[16] Katchalski M., McCuaig W., Seager S.: Ordered colourings.Discrete Math. 142 (1995), 141–154. Zbl 0842.05032, MR 1341442, 10.1016/0012-365X(93)E0216-Q; reference:[17] Lewis P.M. II, Stearns R.E., Hartmanis J.: Memory bounds for recognition of context-free and context-sensitive languages.Proceedings of the Sixth Annual Symposium on Switching Circuit Theory and Logical Design, Ann Arbor, MI, 1965, pp. 191–202. Zbl 0272.68054; reference:[18] Lipton R.J., Tarjan R.E.: A separator theorem for planar graphs.SIAM J. Appl. Math. 36 (1979), no. 2, 177–189. Zbl 0432.05022, MR 0524495, 10.1137/0136016; reference:[19] Nešetřil J., Ossona de Mendez P.: Tree-depth, subgraph coloring and homomorphism bounds.European J. Combin. 27 (2006), 1022–1041. MR 2226435, 10.1016/j.ejc.2005.01.010; reference:[20] Nešetřil J., Ossona de Mendez P., Wood D.R.: Characterisations and examples of graph classes with bounded expansion.CoRR abs/0902.3265 (2009).; reference:[21] Pach J., Tóth G.: Conflict Free Colorings.Discrete and Computational Geometry, The Goodman-Pollack Festschrift, Springer, Berlin, 2003, pp. 665–671. MR 2038496; reference:[22] Pezarski A., Zmarz M.: Non-repetitive $3$-coloring of subdivided graphs.Electron. J. Combin. 16 (2009), N15. Zbl 1165.05325, MR 2515755; reference:[23] Prouhet E.: Mémoire sur quelques relations entre les puissances des nombres.Comptes Rendus de l'Académie des Sciences, Paris, Série I 33 (1851), 225.; reference:[24] Schäffer A.A.: Optimal node ranking of trees in linear time.Inform. Process. Lett. 33 (1989), no. 2, 91–96. MR 1031599, 10.1016/0020-0190(89)90161-0; reference:[25] Thue A.: Über unendliche Zeichenreihen.Norske vid. Selsk. Skr. Mat. Nat. Kl 7 (1906), 1–22.

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Academic Journal

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Relation: mr:MR2493943; zbl:Zbl 1212.05076; reference:[1] Alon M., Marshall T.H.: Homomorphisms of edge-colored graphs and Coxeter groups.J. Algebraic Combin. 8 (1998), 5-13. Zbl 0911.05034, MR 1635549, 10.1023/A:1008647514949; reference:[2] Borodin O.V.: On acyclic colorings of planar graphs.Discrete Math. 25 (1979), 211-236. Zbl 0406.05031, MR 0534939, 10.1016/0012-365X(79)90077-3; reference:[3] Borodin O.V., Kostochka A.V., Nešetřil J., Raspaud A., Sopena E.: On the maximum average degree and the oriented chromatic number of a graph.Discrete Math. 206 (1999), 1-3 77-89. MR 1665387, 10.1016/S0012-365X(98)00393-8; reference:[4] Nešetřil J., Raspaud A.: Colored homomorphisms of colored mixed graphs.J. Combin. Theory Ser. B 80 (2000), 1 147-155. MR 1778206, 10.1006/jctb.2000.1977; reference:[5] Ochem P.: Negative results on acyclic improper colorings.EuroComb 2005. Berlin, September 5-9, 2005. DMTCS Conference Volume AE (2005), pp.357-362.; reference:[6] Sopena E.: The chromatic number of oriented graphs.J. Graph Theory 25 (1997), 3 191-205. Zbl 0874.05026, MR 1451297, 10.1002/(SICI)1097-0118(199707)25:33.0.CO;2-G; reference:[7] Sopena E.: Oriented graph coloring.Discrete Math. 229 (2001), 359-369. Zbl 0971.05039, MR 1815613, 10.1016/S0012-365X(00)00216-8

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Academic Journal

Authors: Tůma, Miroslav

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Relation: mr:MR0944781; zbl:Zbl 0658.65058; reference:[1] T. F. Coleman J. J. Moré: Estimation of Sparse Hessian Matrices and Graph Coloring Problems.Math. Prog. 28 (1984), 243-270. MR 0736293, 10.1007/BF02612334; reference:[2] G. C. Everstine: A Comparison of Three Resequencing Algorithms for the Reduction of Matrix Profile and Wavefront.International Journal on Numerical Methods in Engineering 14 (1979), 837-853. Zbl 0401.73082, 10.1002/nme.1620140606; reference:[3] A. George J. W. H. Liu: Computer Solution of Large Sparse Positive Definite Systems.Prentice-Hall, Inc. Englewood Cliffs. N. J. 07632, 1981. MR 0646786; reference:[4] P. Hanzálek J. Hřebíček J. Kučera: A Conversational Program System for Mathematical Optimization.Computer Physics Communications 41 (1986), 403 - 408. 10.1016/0010-4655(86)90080-9; reference:[5] D. M. Matula L. L. Beck: Smallest-last Ordering and Clustering and Graph Coloring Algorithms.JACM 30 (1983), 417-427. MR 0709826, 10.1145/2402.322385; reference:[6] S. T. McCormick: Optimal Approximation of Sparse Hessians and its Equivalence to a Graph Coloring Problem.Math. Prog. 26 (1983), 153-171. Zbl 0507.65027, MR 0700644, 10.1007/BF02592052; reference:[7] M. J. D. Powell, Ph. L. Toint: On the Estimation of Sparse Hessian Matrices.SIAM on Num. Anal. 16 (1979), 1060-1074. Zbl 0426.65025, MR 0551326, 10.1137/0716078; reference:[8] M. N. Thapa: Optimization of Unconstrained Functions with Sparse Hessian Matrices: Newton-type Methods.Math. Prog. 19 (1984), 156-186. Zbl 0538.49023, MR 0745406; reference:[9] O. C. Zienkiewicz: The Finite Element Method.McGraw Hill, London, 1977. Zbl 0435.73072