Coloring Vertices and Edges of a Path by Nonempty Subsets of a Set
نویسنده
چکیده
A graph G is strongly set colorable if V (G) ∪ E(G) can be assigned distinct nonempty subsets of a set of order n, where |V (G)| + |E(G)| = 2n − 1, such that each edge is assigned the symmetric difference of its end vertices. The principal result is that the path P2n−1 is strongly set colorable for n ≥ 5, disproving a conjecture of S.M. Hegde. We also prove another conjecture of S.M. Hegde on a related type of set coloring of complete bipartite graphs.
منابع مشابه
Coloring vertices and edges of a graph by nonempty subsets of a set
A graph G is strongly set colorable if V (G) ∪ E(G) can be assigned distinct nonempty subsets of a set of order n, where |V (G)| + |E(G)| = 2n − 1, such that each edge is assigned the symmetric difference of its end vertices. The principal result is that the path P2n−1 is strongly set colorable for n ≥ 5, disproving a conjecture of S.M. Hegde. We also prove another conjecture of Hegde on a rela...
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تاریخ انتشار 2008