Mathematics – Combinatorics
Scientific paper
2011-08-25
Mathematics
Combinatorics
Scientific paper
A graph is pseudo-outerplanar if each of its blocks has an embedding in the plane so that the vertices lie on a fixed circle and the edges lie inside the disk of this circle with each of them crossing at most one another. In this paper, the total coloring conjecture is completely confirmed for pseudo-outerplanar graphs. In particular, it is proved that the total chromatic number of every pseudo-outerplanar graph with maximum degree $\Delta\geq 5$ is $\Delta+1$.
Liu Guizhen
Zhang Xin
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