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A characterization of tight ()-stable graphs
Yuqi Xu, Weihua Yang, Xiaxia Guan
Let k and l be two non-negative integers with k > l. A graph G is (k,l)-stable if alpha(G - S) >= alpha(G) - l for every subset S of V(G) with |S| = k, where alpha(G) denotes the i…
A stability result for -free graphs
Sijie Ren, Jian Wang, Shipeng Wang +1
A graph is called -free if it does not contain any cycle of length . In 1981, Haggkvist, Faudree and Schelp showed that every -vertex triangle-free graph wit…
Counterexamples to Gerbner's Conjecture on Stability of Maximal -free Graphs
Jian Wang, Shipeng Wang, Weihua Yang
Let be an -color critical graph with , that is, and there is an edge in such that . Gerbner recently conjectured that every -ver…
A -decomposition of the -fold line graph of
Yifan Zhao, Yulong Wei, Weihua Yang
The small cycle decompositions of line graph (-fold line graph) of complete graphs and complete bipartite graphs are studied by many papers. In particular, Colby and Rodger obta…
Planar graphs without cycles of length from 4 to 7 are near-bipartite
Lili Hao, Weihua Yang, Shuang Zhao
A graph is near-bipartite if its vertex set can be partitioned into an independent set and a set which induces a forest. In this paper, planar graphs without cycles of length from…
On the regular 2-connected 2-path Hamiltonian graphs
Xia Li, Weihua Yang
A graph is -path Hamiltonian if every path of length not exceeding is contained in a Hamiltonian cycle. It is well known that a 2-connected, -regular graph on at…