Bibliographic Details
| Title: |
On the Perfect Matchings of Near Regular Graphs. |
| Authors: |
Hou, Xinmin1 xmhou@ustc.edu.cn |
| Superior Title: |
Graphs & Combinatorics. Nov2011, Vol. 27 Issue 6, p865-869. 5p. |
| Subject Terms: |
*MATCHING theory, *GRAPH theory, *MATHEMATICAL proofs, *MATHEMATICAL series, *MATHEMATICAL analysis, *NUMERICAL analysis, *COMBINATORICS |
| Abstract: |
Let k, h be positive integers with k ≤ h. A graph G is called a [ k, h]-graph if k ≤ d( v) ≤ h for any $${v \in V(G)}$$. Let G be a [ k, h]-graph of order 2 n such that k ≥ n. Hilton (J. Graph Theory 9:193-196, ) proved that G contains at least $${\lfloor k/3\rfloor}$$ disjoint perfect matchings if h = k. Hilton's result had been improved by Zhang and Zhu (J. Combin. Theory, Series B, 56:74-89, ), they proved that G contains at least $${\lfloor k/2\rfloor}$$ disjoint perfect matchings if k = h. In this paper, we improve Hilton's result from another direction, we prove that Hilton's result is true for [ k, k + 1]-graphs. Specifically, we prove that G contains at least $${\lfloor\frac{n}3\rfloor+1+(k-n)}$$ disjoint perfect matchings if h = k + 1. [ABSTRACT FROM AUTHOR] |
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| Database: |
Academic Search Premier |