On Cycles through Vertices of Large Semidegree in Digraphs

S. Kh. Darbinyan; I. A. Karapetyan

On Cycles through Vertices of Large Semidegree in Digraphs

Combinatorics 2014-04-24 v1

Authors: S. Kh. Darbinyan , I. A. Karapetyan

Abstract

Let $D$ be a strong digraph on $n=2m+1\geq 5$ vertices. In this paper we show that if $D$ contains a cycle of length $n-1$ , then $D$ has also a cycle which contains all vertices with in-degree and out-degree at least $m$ (unless some extremal cases).

Keywords

digraph cycle semidegree strong digraph extremal graph theory

Cite

@article{arxiv.1404.5782,
  title  = {On Cycles through Vertices of Large Semidegree in Digraphs},
  author = {S. Kh. Darbinyan and I. A. Karapetyan},
  journal= {arXiv preprint arXiv:1404.5782},
  year   = {2014}
}

Comments

13 pages

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