On the connection between chromatic number, maximal clique and minimal degree of a graph

B. Andrásfai, P. Erdős, V. T. Sós

Research output: Contribution to journalArticle

91 Citations (Scopus)

Abstract

Let Gn be a graph of n vertices, having chromatic number r which contains no complete graph of r vertices. Then Gn contains a vertex of degree not exceeding n(3r-7)/(3r-4). The result is essentially best possible.

Original languageEnglish
Pages (from-to)205-218
Number of pages14
JournalDiscrete Mathematics
Volume8
Issue number3
DOIs
Publication statusPublished - 1974

Fingerprint

Maximal Clique
Chromatic number
Complete Graph
Graph in graph theory
Vertex of a graph

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

On the connection between chromatic number, maximal clique and minimal degree of a graph. / Andrásfai, B.; Erdős, P.; Sós, V. T.

In: Discrete Mathematics, Vol. 8, No. 3, 1974, p. 205-218.

Research output: Contribution to journalArticle

@article{70ec67bf083a4bffa6609e22cb8f972b,
title = "On the connection between chromatic number, maximal clique and minimal degree of a graph",
abstract = "Let Gn be a graph of n vertices, having chromatic number r which contains no complete graph of r vertices. Then Gn contains a vertex of degree not exceeding n(3r-7)/(3r-4). The result is essentially best possible.",
author = "B. Andr{\'a}sfai and P. Erdős and S{\'o}s, {V. T.}",
year = "1974",
doi = "10.1016/0012-365X(74)90133-2",
language = "English",
volume = "8",
pages = "205--218",
journal = "Discrete Mathematics",
issn = "0012-365X",
publisher = "Elsevier",
number = "3",

}

TY - JOUR

T1 - On the connection between chromatic number, maximal clique and minimal degree of a graph

AU - Andrásfai, B.

AU - Erdős, P.

AU - Sós, V. T.

PY - 1974

Y1 - 1974

N2 - Let Gn be a graph of n vertices, having chromatic number r which contains no complete graph of r vertices. Then Gn contains a vertex of degree not exceeding n(3r-7)/(3r-4). The result is essentially best possible.

AB - Let Gn be a graph of n vertices, having chromatic number r which contains no complete graph of r vertices. Then Gn contains a vertex of degree not exceeding n(3r-7)/(3r-4). The result is essentially best possible.

UR - http://www.scopus.com/inward/record.url?scp=0008740710&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0008740710&partnerID=8YFLogxK

U2 - 10.1016/0012-365X(74)90133-2

DO - 10.1016/0012-365X(74)90133-2

M3 - Article

AN - SCOPUS:0008740710

VL - 8

SP - 205

EP - 218

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 3

ER -