Heavy subgraph conditions for longest cycles to be heavy in graphs

Details Heavy subgraph conditions for longest cycles to be heavy in graphs Heavy subgraph conditions for longest cycles to be heavy in graphs

2011-09-21

arxiv.org/abs/1109.4675v1

Mathematics

Combinatorics

Scientific paper

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 paper, we characterize the graphs which contain no heavy cycles. For a given graph $H$, we say that $G$ is $H$-\emph{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.

Affiliated with

Also associated with

No associations

Rating

Heavy subgraph conditions for longest cycles to be heavy in graphs does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Heavy subgraph conditions for longest cycles to be heavy in graphs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Heavy subgraph conditions for longest cycles to be heavy in graphs will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-261885