Equitable total coloring of corona of cubic graphs

Hanna Furmanczyk
University of Gdansk

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Minisymposium: VERTEX COLOURINGS AND FORBIDDEN SUBGRAPHS

Content: The minimum number of total independent sets of $V \cup E$ of graph $G(V,E)$ is called the \emph{total chromatic number} of $G$, denoted by $\chi''(G)$. If difference of cardinalities of any two total independent sets is at most one, then the minimum number of total independent partition sets of $V \cup E$ is called the \emph{equitable total chromatic number}, and denoted by $\chi''_=(G)$. In the talk we consider equitable total coloring of corona of cubic graphs, $G \circ H$. It turns out that, independly on equitable total chromatic numbers of $G$ and $H$, equitable total chromatic number of corona $G \circ H$ is equal to $\Delta(G \circ H) +1$. Thereby, we confirm TCC and ETCC conjectures for coronas of cubic graphs. As a direct consequence we get that all coronas of cubic graphs are of Type 1.

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