Strong edge-coloring for cubic Halin graphs
Journal
Discrete Mathematics
Journal Volume
312
Journal Issue
8
Pages
1468-1475
Date Issued
2012
Author(s)
Abstract
A strong edge-coloring of a graph G is a function that assigns to each edge a color such that two edges within distance two apart must receive different colors. The minimum number of colors used in a strong edge-coloring is the strong chromatic index of G. Lih and Liu (2011) [14] proved that the strong chromatic index of a cubic Halin graph, other than two special graphs, is 6 or 7. It remains an open problem to determine which of such graphs have strong chromatic index 6. Our article is devoted to this open problem. In particular, we disprove a conjecture of Shiu et al. (2006) [18] that the strong chromatic index of a cubic Halin graph with characteristic tree a caterpillar of odd leaves is 6. © 2012 Elsevier B.V. All rights reserved.
Type
journal article