Coloring vertices and edges of a graph by nonempty subsets of a set
نویسندگان
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.
منابع مشابه
Further results on proper and strong set colorings of graphs
A set coloring α of a graph G is defined as an assignment of distinct subsets of a finite set X of colors to the vertices of G such that all the colors of the edges which are obtained as the symmetric differences of the sets assigned to their end-vertices are distinct. Additionally, if all the sets on the vertices and edges of G form the set of all nonempty subsets of X, then the coloring α is ...
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عنوان ژورنال:
- Eur. J. Comb.
دوره 32 شماره
صفحات -
تاریخ انتشار 2011