Triangle-free partial graphs and edge covering theorems

J. Lehel, Z. Tuza

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

In section 1 some lower bounds are given for the maximal number of edges ofa (p - 1)- colorable partial graph. Among others we show that a graph on n vertices with m edges has a (p-1)-colorable partial graph with at least mTn.p/(n2) edges, where Tn.p denotes the so called Turán number. These results are used to obtain upper bounds for special edge covering numbers of graphs. In Section 2 we prove the following theorem: If G is a simple graph and μ is the maximal cardinality of a triangle-free edge set of G, then the edges of G can be covered by μ triangles and edges. In Section 3 related questions are examined.

Original languageEnglish
Pages (from-to)59-65
Number of pages7
JournalDiscrete Mathematics
Volume39
Issue number1
DOIs
Publication statusPublished - 1982

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Triangle-free
Covering
Partial
Graph in graph theory
Theorem
Covering number
Simple Graph
Triangle
Cardinality
Lower bound
Upper bound
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ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Triangle-free partial graphs and edge covering theorems. / Lehel, J.; Tuza, Z.

In: Discrete Mathematics, Vol. 39, No. 1, 1982, p. 59-65.

Research output: Contribution to journalArticle

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