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Heavy Subgraph Conditions for Longest Cycles to Be Heavy in Graphs

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Lia B., Zhang S.

Discussiones Mathematicae Graph Theory

2016

tom 36

nr 2

383-392

Let G be a graph on n vertices. A vertex of G with degree at least n/2 is called a heavy vertex, and a cycle of G which contains all the heavy vertices of G is called a heavy cycle. In this note, we characterize graphs which contain no heavy cycles. For a given graph H, we say that G is H-heavy if every induced subgraph of G isomorphic to H contains two nonadjacent vertices with degree sum at least n. We find all the connected graphs S such that a 2-connected graph G being S-heavy implies any longest cycle of G is a heavy cycle.

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1 Discussiones Mathematicae Graph Theory

1 Lia B.

1 Zhang S.

1 2016

Wyniki wyszukiwania

Heavy Subgraph Conditions for Longest Cycles to Be Heavy in Graphs