# Some new sufficient conditions for $2p$-Hamilton-biconnectedness of graphs

@article{Chen2017SomeNS, title={Some new sufficient conditions for \$2p\$-Hamilton-biconnectedness of graphs}, author={Ming-Zhu Chen and Xiaodong Zhang}, journal={arXiv: Combinatorics}, year={2017} }

A balanced bipartite graph $G$ is said to be $2p$-Hamilton-biconnected if for any balanced subset $W$ of size $2p$ of $V(G)$, the subgraph induced by $V(G)\backslash W$ is Hamilton-biconnected. In this paper, we prove that "Let $p\geq0$ and $G$ be a balanced bipartite graph of order $2n$ with minimum degree $\delta(G)\geq k$, where $n\geq 2k-p+2$ and $k\geq p$. If the number of edges $ e(G)>n(n-k+p-1)+(k+2)(k-p+1), $ then $G$ is $2p$-Hamilton-biconnected except some exceptions." Furthermore… Expand

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