Research Article

Forbidden subgraphs for graphs with (near) perfect matching to be Hamiltonian

Published in: Quaestiones Mathematicae
Volume 44 , issue 7 , 2021 , pages: 857–867

DOI: 10.2989/16073606.2020.1752840

Author(s): Xiaojing Yang , P.R. of China , Liming Xiong , P.R. of China

Keywords: 05C38 , 05C45 , 05C38 , 05C45

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.

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