Let G be a graph. If there exists a spanning subgraph F such that dF(x) ∈ {1,3,…2n – 1}, then is called to be (1,2n – 1)-odd factor of G. Some sufficient and necessary conditions are given for G – U to have (1,2n...Let G be a graph. If there exists a spanning subgraph F such that dF(x) ∈ {1,3,…2n – 1}, then is called to be (1,2n – 1)-odd factor of G. Some sufficient and necessary conditions are given for G – U to have (1,2n – 1)-odd factor where U is any subset of V(G) such that |U| = k.展开更多
A connected graph G is said to be a factor-critical graph if G - v has a perfect matching for every vertex v of G. In this paper, the 2-connected factor-critical graph G which has exactly ｜E（G）｜＋ 1 maximum matchi...A connected graph G is said to be a factor-critical graph if G - v has a perfect matching for every vertex v of G. In this paper, the 2-connected factor-critical graph G which has exactly ｜E（G）｜＋ 1 maximum matchings is characterized.展开更多
The maximum matching graph M（G） of a graph G is a simple graph whose vertices are the maximum matchings of G and where two maximum matchings are adjacent in M（G） if they differ by exactly one edge. In this paper, ...The maximum matching graph M（G） of a graph G is a simple graph whose vertices are the maximum matchings of G and where two maximum matchings are adjacent in M（G） if they differ by exactly one edge. In this paper, we prove that if a graph is isomorphic to its maximum matching graph, then every block of the graph is an odd cycle.展开更多
文摘Let G be a graph. If there exists a spanning subgraph F such that dF(x) ∈ {1,3,…2n – 1}, then is called to be (1,2n – 1)-odd factor of G. Some sufficient and necessary conditions are given for G – U to have (1,2n – 1)-odd factor where U is any subset of V(G) such that |U| = k.
基金supported by the National Natural Science Foundation of China(No.11551003)the Scientific research fund of the Science and Technology Program of Guangzhou,China(No.201510010265)the Qinghai Province Natural Science Foundation(No.2015-ZJ-911)
文摘A connected graph G is said to be a factor-critical graph if G - v has a perfect matching for every vertex v of G. In this paper, the 2-connected factor-critical graph G which has exactly ｜E（G）｜＋ 1 maximum matchings is characterized.
基金Supported by National Natural Science of Foundation of China (Grant Nos. 10531070, 10721101)KJCX YW-S7 of CAS
文摘The maximum matching graph M（G） of a graph G is a simple graph whose vertices are the maximum matchings of G and where two maximum matchings are adjacent in M（G） if they differ by exactly one edge. In this paper, we prove that if a graph is isomorphic to its maximum matching graph, then every block of the graph is an odd cycle.
