The star edge coloring of cubic Halin graphs with star chromatic index $ 5 $
Abstract
The star chromatic index of a graph $ G $, denoted by $ \chi'_{st}(G) $, is the minimum number of colors needed to properly color the edges of $ G $ such that no path or cycle of length four is bi-colored. Casselgren et al. and Hou et al. independently proved that the star chromatic index of a cubic Halin graph, except in the case of a special graph, is at most $ 6 $. It remains an open problem to determine which of such graphs have star chromatic index $ 5 $. In this paper, we show that if $ G\ne N_{e_2} $ is a cubic Halin graph whose tree is a caterpillar or a complete tree, then $ \chi'_{st}(G) = 5 $.
Fields of Study & Subjects
Graph Labeling and Dimension Problems
Advanced Graph Theory Research
Limits and Structures in Graph Theory
Publication details
- Journal / source
- AIMS Mathematics
- Volume
- 11
- Issue
- 1
- Pages
- 3132–3141
- Publication date
- 1 January 2026