Colorful induced subgraphs

Henry Kierstead, W. T. Trotter

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

A colored graph is a graph whose vertices have been properly, though not necessarily optimally colored, with integers. Colored graphs have a natural orientation in which edges are directed from the end point with smaller color to the end point with larger color. A subgraph of a colored graph is colorful if each of its vertices has a distinct color. We prove that there exists a function f(k, n) such that for any colored graph G, if χ(G)>f(ω(G), n) then G induces either a colorful out directed star with n leaves or a colorful directed path on n vertices. We also show that this result would be false if either alternative was omitted. Our results provide a solution to Problem 115, Discrete Math. 79.

Original languageEnglish (US)
Pages (from-to)165-169
Number of pages5
JournalDiscrete Mathematics
Volume101
Issue number1-3
DOIs
StatePublished - May 29 1992

Fingerprint

Colored Graph
Induced Subgraph
Color
End point
Stars
Subgraph
Star
Leaves
Distinct
Path
Integer
Alternatives
Graph in graph theory

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Colorful induced subgraphs. / Kierstead, Henry; Trotter, W. T.

In: Discrete Mathematics, Vol. 101, No. 1-3, 29.05.1992, p. 165-169.

Research output: Contribution to journalArticle

Kierstead, Henry ; Trotter, W. T. / Colorful induced subgraphs. In: Discrete Mathematics. 1992 ; Vol. 101, No. 1-3. pp. 165-169.
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