A simple graph G is induced matching extendable,shortly IM\|extendable,if every induced matching of G is included in a perfect matching of G .The degree conditions of IM\|extendable graphs are researched in...A simple graph G is induced matching extendable,shortly IM\|extendable,if every induced matching of G is included in a perfect matching of G .The degree conditions of IM\|extendable graphs are researched in this paper.The main results are as follows:\;(1) 2n/32n/32n/32n/3 is the minimum integer δ such that every graph with minimum degree at least δ is IM\|extendable,where n=|V(G)|≥6 is even.\;(2) is the minimum integer δ such that every graph with minimum degree at least δ is IM\|extendable,where n=|V(G)|≥6 is even.\;(2) (2n-2)/3 is the minimum integer k such that, for k′≥k ,every k ′ regular graph with vertex number n is IM\|extendable,where n=|V(G)| is even, n ≥8 and n ≠10.展开更多
文摘A simple graph G is induced matching extendable,shortly IM\|extendable,if every induced matching of G is included in a perfect matching of G .The degree conditions of IM\|extendable graphs are researched in this paper.The main results are as follows:\;(1) 2n/32n/32n/32n/3 is the minimum integer δ such that every graph with minimum degree at least δ is IM\|extendable,where n=|V(G)|≥6 is even.\;(2) is the minimum integer δ such that every graph with minimum degree at least δ is IM\|extendable,where n=|V(G)|≥6 is even.\;(2) (2n-2)/3 is the minimum integer k such that, for k′≥k ,every k ′ regular graph with vertex number n is IM\|extendable,where n=|V(G)| is even, n ≥8 and n ≠10.
