0333 - 3590 Backbone colorings for networks
نویسندگان
چکیده
We introduce and study backbone colorings, a variation on classical vertex colorings: 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 V → {1, 2, . . .} of G in which the colors assigned to adjacent vertices in H differ by at least two. We study the cases where the backbone is either a spanning tree or a spanning path. We show that for tree backbones of G the number of colors needed for a backbone coloring of G can roughly differ by a multiplicative factor of at most 2 from the chromatic number χ(G); for path backbones this factor is roughly 3 2 . For the special case that G is a split graph the difference from χ(G) is at most an additive constant 2 or 1, for tree backbones and path backbones, respectively. We show that the computational complexity of the problem ‘Given a graph G, a spanning tree T of G, and an integer `, is there a backbone coloring for G and T with at most ` colors?’ jumps from polynomial to NP-complete between ` = 4 (easy for all spanning trees) and ` = 5 (difficult even for spanning paths).
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تاریخ انتشار 2003