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- W2950075601 abstract "For maximal planar graphs of order $ngeq 4$, we prove that a vertex--coloring containing no rainbow faces uses at most $lfloorfrac{2n-1}{3}rfloor$ colors, and this is best possible. For maximal graph embedded on the projective plane, we obtain the analogous best bound $lfloorfrac{2n+1}{3}rfloor$. The main ingredients in the proofs are classical homological tools. By considering graphs as topological spaces, we introduce the notion of a null coloring, and prove that for any graph $G$ a maximal null coloring $f$ is such that the quotient graph $G/f$ is a forest." @default.
- W2950075601 created "2019-06-27" @default.
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- W2950075601 date "2012-10-25" @default.
- W2950075601 modified "2023-10-01" @default.
- W2950075601 title "Null and non--rainbow colorings of projective plane and sphere triangulations" @default.
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