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- W3157143338 abstract "Rainbow coloring problems, of noteworthy applications in Information Security, have been receiving much attention in the last years in Combinatorics. In particular, the rainbow connection number of a connected graph G, denoted rc(G), is the least k for which G admits a (not necessarily proper) k-edge-coloring such that between any pair of vertices there is a path whose edge colors are all distinct. When G is disconnected, we define rc(G)=∞. A graph G is rainbow critical if the deletion of any edge of G increases rc(G). In this paper we determine the rainbow connection number for the shadow graphs of paths, some circulant graphs, and some Cartesian products involving cycles and paths. We also determine conditions for the rainbow criticality and non-criticality of wheels, fans, and some Cartesian products involving cycles, paths, pans, and complete graphs." @default.
- W3157143338 created "2021-05-10" @default.
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- W3157143338 date "2022-12-01" @default.
- W3157143338 modified "2023-09-23" @default.
- W3157143338 title "Rainbow connectivity and rainbow criticality on graph classes" @default.
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- W3157143338 doi "https://doi.org/10.1016/j.dam.2021.04.017" @default.
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