Bibliographic Details
| Title: |
Rainbow subgraphs in edge‐colored complete graphs: Answering two questions by Erdős and Tuza. |
| Authors: |
Axenovich, Maria1 (AUTHOR), Clemen, Felix C.1 (AUTHOR) felix.clemen@kit.edu |
| Superior Title: |
Journal of Graph Theory. May2024, Vol. 106 Issue 1, p57-66. 10p. |
| Subject Terms: |
*SUBGRAPHS, *GRAPH coloring, *RAINBOWS, *COMPLETE graphs, *RAMSEY numbers |
| Abstract: |
An edge‐coloring of a complete graph with a set of colors C $C$ is called completely balanced if any vertex is incident to the same number of edges of each color from C $C$. Erdős and Tuza asked in 1993 whether for any graph F $F$ on ℓ $\ell $ edges and any completely balanced coloring of any sufficiently large complete graph using ℓ $\ell $ colors contains a rainbow copy of F $F$. This question was restated by Erdős in his list of "Some of my favourite problems on cycles and colourings." We answer this question in the negative for most cliques F=Kq $F={K}_{q}$ by giving explicit constructions of respective completely balanced colorings. Further, we answer a related question concerning completely balanced colorings of complete graphs with more colors than the number of edges in the graph F $F$. [ABSTRACT FROM AUTHOR] |
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| Database: |
Academic Search Premier |
