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arXiv · 1203.6143

Some Results on incidence coloring, star arboricity and domination number

Pak Kiu Sun·Wai Chee Shiu
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Abstract

Two inequalities bridging the three isolated graph invariants, incidence chromatic number, star arboricity and domination number, were established. Consequently, we deduced an upper bound and a lower bound of the incidence chromatic number for all graphs. Using these bounds, we further reduced the upper bound of the incidence chromatic number of planar graphs and showed that cubic graphs with orders not divisible by four are not 4-incidence colorable. The incidence chromatic numbers of Cartesian product, join and union of graphs were also determined.

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Pak Kiu Sun, Wai Chee Shiu. 2012-03-28. Some Results on incidence coloring, star arboricity and domination number. https://arxiv.org/abs/1203.6143

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