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- W2585997002 abstract "Graph coloring problem asks to assign a color to every vertex such that adjacent vertices get different color. There have been different ways to generalize classical graph coloring problem. Among them, we study (k, i)-coloring of a graph. In (k, i)-coloring, every vertex is assigned a set of k colors so that adjacent vertices share at most i colors between them. The (k, i)-chromatic number of a graph is the minimum number of total colors used to assign a proper (k, i)-coloring. It is clear that (1, 0)-coloring is equivalent to the classical graph coloring problem. We extend the study of exact and parameterized algorithms for classical graph coloring problem to (k, i)-coloring of graphs. Given a graph with n vertices and m edges, we design algorithms that take(mathcal {O}(2^{kn}cdot n^{{mathcal O}(1)})) time to determine the (k, 0)-chromatic number.(mathcal {O}(4^n cdot n^{{mathcal O}(1)})) time to determine the (k, k-1)-chromatic number.(mathcal {O}(2^{kn}cdot k^{im} cdot n^{{mathcal O}(1)})) time to determine the (k, i)-chromatic number." @default.
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- W2585997002 date "2017-01-01" @default.
- W2585997002 modified "2023-09-23" @default.
- W2585997002 title "Exact and Parameterized Algorithms for (k, i)-Coloring" @default.
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- W2585997002 doi "https://doi.org/10.1007/978-3-319-53007-9_25" @default.
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