EEMCS

Full text available as:

PDF - Univ. of Twente only - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader 401 Kb

Official URL: http://dx.doi.org/10.1016/j.aml.2008.04.003

Abstract

For positive integers and , a conditional -coloring of a graph is a proper -coloring of the vertices of such that every vertex of degree in is adjacent to vertices with at least different colors. The smallest integer for which a graph has a conditional -coloring is called the th-order conditional chromatic number, and is denoted by . It is easy to see that conditional coloring is a generalization of traditional vertex coloring (the case ). In this work, we consider the complexity of the conditional colorability of graphs. Our main result is that conditional (3,2)-colorability remains NP-complete when restricted to planar bipartite graphs with maximum degree at most 3 and arbitrarily high girth. This differs considerably from the well-known result that traditional 3-colorability is polynomially solvable for graphs with maximum degree at most 3. On the other hand we show that (3,2)-colorability is polynomially solvable for graphs with bounded tree-width. We also prove that some other well-known complexity results for traditional coloring still hold for conditional coloring.

Export this item as:

• BibTeX
• XML

To request a copy of the PDF please email us request copy

To correct this item please ask your editor

Repository Staff Only: edit this item