Coloring vertices and edges of a graph by nonempty subsets of a set

نویسندگان

  • Paul N. Balister
  • Ervin Györi
  • Richard H. Schelp
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 Hegde on a related type of set coloring of complete bipartite graphs.

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عنوان ژورنال:
  • Eur. J. Comb.

دوره 32  شماره 

صفحات  -

تاریخ انتشار 2011