On uniquely 3-colorable graphs

Chong Yun Chao; Zhibo Chen

doi:10.1016/0012-365X(93)90220-N

On uniquely 3-colorable graphs

Chong Yun Chao, Zhibo Chen

Penn State Greater Allegheny

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

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 K_k with k vertices for any integer k≥3.

Original language	English (US)
Pages (from-to)	21-27
Number of pages	7
Journal	Discrete Mathematics
Volume	112
Issue number	1-3
DOIs	https://doi.org/10.1016/0012-365X(93)90220-N
State	Published - Mar 25 1993

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/0012-365X(93)90220-N

Cite this

@article{18337d9fd85d41699c1b43e49f2cb609,

title = "On uniquely 3-colorable graphs",

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.",

author = "Chao, \{Chong Yun\} and Zhibo Chen",

year = "1993",

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AU - Chao, Chong Yun

AU - Chen, Zhibo

PY - 1993/3/25

Y1 - 1993/3/25

N2 - 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.

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.

UR - https://www.scopus.com/pages/publications/38249002114

UR - https://www.scopus.com/inward/citedby.url?scp=38249002114&partnerID=8YFLogxK

U2 - 10.1016/0012-365X(93)90220-N

DO - 10.1016/0012-365X(93)90220-N

M3 - Article

AN - SCOPUS:38249002114

SN - 0012-365X

VL - 112

SP - 21

EP - 27

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 1-3

ER -

On uniquely 3-colorable graphs

Abstract

All Science Journal Classification (ASJC) codes

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