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- W2963590147 abstract "Let G be a graph such that each edge has its list of available colors, and assume that each list is a subset of the common set consisting of k colors. Suppose that we are given two list edge-colorings (f_0) and (f_r) of G, and asked whether there exists a sequence of list edge-colorings of G between (f_0) and (f_r) such that each list edge-coloring can be obtained from the previous one by changing a color assignment of exactly one edge. This problem is known to be PSPACE-complete for every integer (k ge 6) and planar graphs of maximum degree three, but any computational hardness was unknown for the non-list variant in which every edge has the same list of k colors. In this paper, we first improve the known result by proving that, for every integer (k ge 4), the problem remains PSPACE-complete even for planar graphs of maximum degree three and bounded bandwidth. Since the problem is known to be solvable in polynomial time if (k le 3), our result gives a sharp analysis of the complexity status with respect to the number k of colors. We then give the first computational hardness result for the non-list variant: for every integer (k ge 5), the non-list variant is PSPACE-complete even for planar graphs of maximum degree k and bandwidth linear in k." @default.
- W2963590147 created "2019-07-30" @default.
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- W2963590147 date "2018-01-01" @default.
- W2963590147 modified "2023-09-24" @default.
- W2963590147 title "The Complexity of (List) Edge-Coloring Reconfiguration Problem" @default.
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- W2963590147 doi "https://doi.org/10.1587/transfun.e101.a.232" @default.
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