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JGT
2010
13 years 5 months ago
2010
While finite cop-win finite graphs possess a good structural characterization, none is known for infinite cop-win graphs. As evidence that such a characterization might not exis...
JGT
2006
13 years 7 months ago
2006
Abstract: A k-tree is a chordal graph with no (k + 2)-clique. An -treepartition of a graph G is a vertex partition of G into `bags,' such that contracting each bag to a single...
JGT
2006
13 years 7 months ago
2006
We study the number F[n; k] of n-vertex graphs that can be written as the edgeunion of k-vertex cliques. We obtain reasonably tight estimates for F[n; k] in the cases (i) k = n-o(...
JGT
2006
13 years 7 months ago
2006
We prove that for every fixed k and 5 and for sufficiently large n, every edge coloring of the hypercube Qn with k colors contains a monochromatic cycle of length 2 . This answer...
JGT
2006
13 years 7 months ago
2006
We find the maximum number of maximal independent sets in two families of graphs. The first family consists of all graphs with n vertices and at most r cycles. The second family i...