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- W2146015910 abstract "Given a graph $G=(V,E)$ and a spanning subgraph $H$ of $G$ (the backbone of $G$), a backbone coloring for $G$ and $H$ is a proper vertex coloring $Vrightarrow {1,2,ldots}$ of $G$ in which the colors assigned to adjacent vertices in $H$ differ by at least two. In a recent paper, backbone colorings were introduced and studied in cases were the backbone is either a spanning tree or a spanning path. Here we study the case where the backbone is a perfect matching. We show that for perfect matching backbones of $G$ the number of colors needed for a backbone coloring of $G$ can roughly differ by a multiplicative factor of at most $frac{4}{3}$ from the chromatic number $chi(G)$. We show that the computational complexity of the problem ``Given a graph $G$ with a perfect matching $M$, and an integer $ell$, is there a backbone coloring for $G$ and $M$ with at most $ell$ colors?'' jumps from polynomial to NP-complete between $ell=3$ and $ell=4$. Finally, we consider the case where $G$ is a planar graph." @default.
- W2146015910 created "2016-06-24" @default.
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- W2146015910 date "2003-01-01" @default.
- W2146015910 modified "2023-10-17" @default.
- W2146015910 title "Backbone colorings along perfect matchings" @default.
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