Induced matching extendable graph powers
J Qian - Graphs and Combinatorics, 2006 - Springer
J Qian
Graphs and Combinatorics, 2006•SpringerA graph G is called induced matching extendable (shortly, IM-extendable) if every induced
matching of G is included in a perfect matching of G. A graph G is called strongly IM-
extendable if every spanning supergraph of G is IM-extendable. The k-th power of a graph
G, denoted by G k, is the graph with vertex set V (G) in which two vertices are adjacent if and
only if the distance between them in G is at most k. We obtain the following two results which
give positive answers to two conjectures of Yuan. Result 1. If a connected graph G with| V …
matching of G is included in a perfect matching of G. A graph G is called strongly IM-
extendable if every spanning supergraph of G is IM-extendable. The k-th power of a graph
G, denoted by G k, is the graph with vertex set V (G) in which two vertices are adjacent if and
only if the distance between them in G is at most k. We obtain the following two results which
give positive answers to two conjectures of Yuan. Result 1. If a connected graph G with| V …
Abstract
A graph G is called induced matching extendable (shortly, IM-extendable) if every induced matching of G is included in a perfect matching of G. A graph G is called strongly IM-extendable if every spanning supergraph of G is IM-extendable. The k-th power of a graph G, denoted by G k , is the graph with vertex set V(G) in which two vertices are adjacent if and only if the distance between them in G is at most k.
We obtain the following two results which give positive answers to two conjectures of Yuan.
Result 1. If a connected graph G with |V(G)| even is locally connected, then G2 is strongly IM-extendable.
Result 2. If G is a 2-connected graph with |V(G)| even, then G3 is strongly IM-extendable.
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