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- W2912339235 abstract "For a graph $G$, the $t$-th power $G^t$ is the graph on $V(G)$ such that two vertices are adjacent if and only if they have distance at most $t$ in $G$; and the $t$-th bi-power $G_B^t$ is the graph on $V(G)$ such that two vertices are adjacent if and only if their distance in $G$ is odd at most $t$. Fleischner's theorem states that the square of every 2-connected finite graph has a Hamiltonian cycle. Georgakopoulos prove that the square of every 2-connected infinite locally finite graph has a Hamiltonian circle. In this paper, we consider the Hamiltonicity of the bi-power of bipartite graphs. We show that for every connected finite bipartite graph $G$ with a perfect matching, $G_B^3$ has a Hamiltonian cycle. We also show that if $G$ is a connected infinite locally finite bipartite graph with a perfect matching, then $G_B^3$ has a Hamiltonian circle." @default.
- W2912339235 created "2019-02-21" @default.
- W2912339235 creator A5070133688 @default.
- W2912339235 date "2019-02-18" @default.
- W2912339235 modified "2023-10-18" @default.
- W2912339235 title "Hamiltonicity of bi-power of bipartite graphs, for finite and infinite cases" @default.
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- W2912339235 doi "https://doi.org/10.48550/arxiv.1902.06403" @default.
- W2912339235 hasPublicationYear "2019" @default.
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