ISSN 1234-3099 (print version)
ISSN 2083-5892 (electronic version)
SCImago Journal Rank (SJR) 2018: 0.763
Rejection Rate (2018-2019): c. 84%
Discussiones Mathematicae Graph Theory 24(1) (2004) 5-21
Department of MathematicsWestern Michigan UniversityKalamazoo, MI 49008, USA
Faculty of Arts and PhilosophyCharles University, Prague nám. J. Palacha 2CZ - 116 38 Praha 1, Czech Republic
for every two distinct vertices u and v of G, where d(u, v) is the distance between u and v. The value
(c) of a radio k-coloring c of G is the maximum color assigned to a vertex of G. The radio k-chromatic number rck
(G) of G is the minimum value of rck
(c) taken over all radio k-colorings c of G. In this paper, radio k-colorings of paths are studied. For the path Pn of order n ≥
9 and n odd, a new improved bound for rcn−
(Pn) is presented. For n ≥
4, it is shown that
Upper and lower bounds are also presented for rck
(Pn) in terms of k when 1 ≤
1. The upper bound is shown to be sharp when 1 ≤
4 and n is sufficiently large.
Keywords: radio k-coloring, radio k-chromatic number.
2000 Mathematics Subject Classification: 05C12, 05C15, 05C78.
Received 16 December 2000Revised 14 November 2002