On uniquely 3-colorable graphs

Chong Yun Chao, Zhibo Chen

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

We show the following. (1) For each integer n≥12, there exists a uniquely 3-colorable graph with n vertices and without any triangles. (2) There exist infinitely many uniquely 3-colorable regular graphs without any triangles. It follows that there exist infinitely many uniquely k-colorable regular graphs having no subgraph isomorphic to the complete graph Kk with k vertices for any integer k≥3.

Original languageEnglish (US)
Pages (from-to)21-27
Number of pages7
JournalDiscrete Mathematics
Volume112
Issue number1-3
DOIs
StatePublished - Mar 25 1993

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Regular Graph
Triangle
Integer
Graph in graph theory
Complete Graph
Subgraph
Isomorphic

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Chao, Chong Yun ; Chen, Zhibo. / On uniquely 3-colorable graphs. In: Discrete Mathematics. 1993 ; Vol. 112, No. 1-3. pp. 21-27.
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On uniquely 3-colorable graphs. / Chao, Chong Yun; Chen, Zhibo.

In: Discrete Mathematics, Vol. 112, No. 1-3, 25.03.1993, p. 21-27.

Research output: Contribution to journalArticle

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AB - We show the following. (1) For each integer n≥12, there exists a uniquely 3-colorable graph with n vertices and without any triangles. (2) There exist infinitely many uniquely 3-colorable regular graphs without any triangles. It follows that there exist infinitely many uniquely k-colorable regular graphs having no subgraph isomorphic to the complete graph Kk with k vertices for any integer k≥3.

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