Abstract

Let G = (V (G), E(G)) be a graph. A set M ⊆ E(G) is a matching if no two edges in M share a common vertex. A matching of G is perfect if it covers every vertex in G. A matching of a graph G with odd order is called a near perfect matching if it has edges. In this paper, we completely characterize the forbidden subgraph and pairs of forbidden subgraphs that force a 2-connected graph with a (near) perfect matching to be hamiltonian.

中文翻译：

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具有（接近）完美匹配为哈密顿量的图的禁止子图

摘要

设G = ( V ( G ) , E ( G )) 是一个图。一组中号⊆È（ģ）是一个匹配，如果在任何两个边缘中号共享一个共同的顶点。如果G覆盖G 中的每个顶点，则匹配是完美的。具有奇数阶的图G 的匹配称为近完美匹配，如果它有边。在本文中，我们完全刻画了禁止子图和成对禁止子图，它们迫使具有（接近）完美匹配的 2 连通图成为哈密顿图。