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<p>A cycle <i>C</i> in a graph <i>G</i> is a <i>forced cycle</i> if <i>G</i> − <i>V</i>(<i>C</i>) has a unique perfect matching. A graph <i>G</i> is <i>cycle-forced</i> if in <i>G</i> either all even cycles or all odd cycles are forced cycles. This paper presents a characterization of cycle-forced bipartite graphs, and as a byproduct, the number of perfect matchings of a cycle-forced bipartite graph is obtained.</p>

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Cycle-forced Bipartite Graphs

  • 期刊论文

  • 发表日期：

    2026年7月7日

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  • Xiang-jing Kong,
  • Yi-pei Zhang,
  • Xiu-mei Wang,
  • Jin-feng Liu

摘要

A cycle C in a graph G is a forced cycle if G − V(C) has a unique perfect matching. A graph G is cycle-forced if in G either all even cycles or all odd cycles are forced cycles. This paper presents a characterization of cycle-forced bipartite graphs, and as a byproduct, the number of perfect matchings of a cycle-forced bipartite graph is obtained.