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Upper Bounds for the Strong Chromatic Index of Halin Graphs

Ziyu HuKo-Wei LihDaphne Der-Fen Liu — 2018

Discussiones Mathematicae Graph Theory

The strong chromatic index of a graph G, denoted by χ′s(G), is the minimum number of vertex induced matchings needed to partition the edge set of G. Let T be a tree without vertices of degree 2 and have at least one vertex of degree greater than 2. We construct a Halin graph G by drawing T on the plane and then drawing a cycle C connecting all its leaves in such a way that C forms the boundary of the unbounded face. We call T the characteristic tree of G. Let G denote a Halin graph with maximum...

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