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Interval edge-colorings of complete graphs and n-dimensional cubes

Interval edge-colorings of complete graphs and n-dimensional cubes,10.1016/j.disc.2010.02.001,Discrete Mathematics,Petros A. Petrosyan

Interval edge-colorings of complete graphs and n-dimensional cubes   (Citations: 2)
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An edge-coloring of a graph G with colors 1,2,…,t is called an interval t-coloring if for each i∈{1,2,…,t} there is at least one edge of G colored by i, and the colors of edges incident to any vertex of G are distinct and form an interval of integers. In this paper we show that if n=p2q, where p is odd, q is nonnegative, and 2n−1≤t≤4n−2−p−q, then the complete graph K2n has an interval t-coloring. We also prove that if n≤t≤n(n+1)2, then the n-dimensional cube Qn has an interval t-coloring.
Journal: Discrete Mathematics - DM , vol. 310, no. 10-11, pp. 1580-1587, 2010
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