Coloring

Author:
James H. Schmerl

Journal:
Trans. Amer. Math. Soc. **354** (2002), 967-974

MSC (2000):
Primary 03E02, 05C62

DOI:
https://doi.org/10.1090/S0002-9947-01-02881-1

Published electronically:
October 31, 2001

MathSciNet review:
1867367

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Abstract | References | Similar Articles | Additional Information

Abstract: If and , then define the graph to be the graph whose vertex set is with two vertices being adjacent iff there are distinct such that . For various and and various , typically or , the graph can be properly colored with colors. It is shown that in some cases such a coloring can also have the additional property that if is an isometric embedding, then the restriction of to is a bijection onto .

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Additional Information

**James H. Schmerl**

Affiliation:
Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269-3009

Email:
schmerl@math.uconn.edu

DOI:
https://doi.org/10.1090/S0002-9947-01-02881-1

Keywords:
Graph coloring,
distance graphs,
Steinhaus property

Received by editor(s):
December 15, 2000

Received by editor(s) in revised form:
May 7, 2001

Published electronically:
October 31, 2001

Article copyright:
© Copyright 2001
American Mathematical Society