2019•MathematicsOpen access

Matching Extendabilities of G = Cm ∨ Pn

Zhi‐hao Hui, Yu Yang, Hua Wang, Xiaojun Sun

Abstract

A graph is considered to be induced-matching extendable (bipartite matching extendable) if every induced matching (bipartite matching) of G is included in a perfect matching of G. The induced-matching extendability and bipartite-matching extendability of graphs have been of interest. By letting G = C m ∨ P n ( m ≥ 3 and n ≥ 1 ) be the graph join of C m (the cycle with m vertices) and P n (the path with n vertices) contains a perfect matching, we find necessary and sufficient conditions for G to be induced-matching extendable and bipartite-matching extendable.

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Key concepts: Bipartite graph, Combinatorics, Matching (statistics), Factor-critical graph, 3-dimensional matching, Mathematics, Complete bipartite graph, Blossom algorithm