Heredity properties of connectedness in edge-coloured complete graphs

Adam Idzik, Z. Tuza

Research output: Contribution to journalArticle

Abstract

If the monochromatic graphs G1 and G2 in a 2-edge-coloured complete graph Km (m ≥ 6) are connected, then there exist at least two vertices x such that the graphs G1\x and G2\x are also connected. Similar theorems are proved for k-edge-coloured complete graphs. They generalize earlier results of Idzik et al. [Discrete Math. 66 (1987) 119-125]. Examples are shown that analogous theorems are no longer true for 3-uniform complete hypergraphs.

Original languageEnglish
Pages (from-to)301-306
Number of pages6
JournalDiscrete Mathematics
Volume235
Issue number1-3
DOIs
Publication statusPublished - May 28 2001

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Edge-colored Graph
Connectedness
Complete Graph
Graph in graph theory
Hypergraph
Theorem
Generalise

Keywords

  • Complete graph
  • Connected graph
  • Edge-colouring
  • r-uniform hypergraph

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Heredity properties of connectedness in edge-coloured complete graphs. / Idzik, Adam; Tuza, Z.

In: Discrete Mathematics, Vol. 235, No. 1-3, 28.05.2001, p. 301-306.

Research output: Contribution to journalArticle

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