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- W2108792210 abstract "A b-coloring is a coloring of the vertices of a graph such that each color class contains a vertex that has a neighbour in all other color classes. The b-chromatic number of a graph G is the largest integer k such that G admits a b-coloring with k colors. A graph is b-perfect if the b-chromatic number is equal to the chromatic number for every induced subgraph H of G . A graph is minimally b-imperfect if it is not b-perfect and every proper induced subgraph is b-perfect. We give a list F of minimally b-imperfect graphs, conjecture that a graph is b-perfect if and only if it does not contain a graph from this list as an induced subgraph, and prove this conjecture for diamond-free graphs, and graphs with chromatic number at most three." @default.
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- W2108792210 date "2009-10-01" @default.
- W2108792210 modified "2023-10-12" @default.
- W2108792210 title "On minimally b-imperfect graphs" @default.
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- W2108792210 doi "https://doi.org/10.1016/j.dam.2009.02.023" @default.
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