Original Articles

ON THE DICHROMATIC INDEX OF A DIGRAPH

Published in: Quaestiones Mathematicae
Volume 19 , issue 1-2 , 1996 , pages: 325–329

DOI: 10.1080/16073606.1996.9631842

Author(s): Frank Harary Department of Computer Science, USA , PaulC. Kainen Department of Computer Science, USA

Keywords: 05C20

Abstract

Let D be a digraph. The arc (u, v) is adjacent to the arc (w, x) if v = w. Let r(D) be the smallest number of arc colors so that no two adjacent arcs have the same color. Let G be the underlying graph of D and let x(G) be its usual chromatic number. We extend a lower bound of Lovász for r(D) by proving that

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