## 3-CONSECUTIVE C-COLORINGS OF GRAPHS

Csilla Bujtás1,  E. Sampathkumar2,  Zsolt Tuza1,3, M.S. Subramanya2  and  Charles Dominic2

1Department of Computer Science
University of Pannonia
H-8200 Veszprém, Egyetem u. 10, Hungary

2Department of Mathematics
University of Mysore, Mysore, India

3Computer and Automation Institute
H-1111 Budapest, Kende u. 13-17, Hungary

## Abstract

A 3-consecutive C-coloring of a graph G = (V,E) is a mapping φ:V→ℕ such that every path on three vertices has at most two colors. We prove general estimates on the maximum number [￣(χ)]3CC(G) of colors in a 3-consecutive C-coloring of G, and characterize the structure of connected graphs with [￣(χ)]3CC(G) ≥ k for k = 3 and k = 4.

Keywords: graph coloring, vertex coloring, consecutive coloring, upper chromatic number.

2010 Mathematics Subject Classification: 05C15, 05C75.

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