Hunter S. Snevily

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The pebbling number of a graph G, f(G), is the least m such that, however m pebbles are placed on the vertices of G, we can move a pebble to any vertex by a sequence of moves, each move taking two pebbles o one vertex and placing one on an adjacent vertex. It is conjectured that for all graphs G and H , f(G H) f(G)f(H). Let Cm and Cn be cycles. We prove(More)
An explicit definition of a 1-factorization of B k (the bipartite graph defined by the kand (k+l)-element subsets of [ 2k+ l ] ) , whose constituent matchings are defined using addition modulo k + 1, is introduced. We show that the matchings are invariant under rotation (mapping under ~r = (1, 2, 3 ..... 2k + 1 )), describe the effect of reflection (mapping(More)
On the van der Waerden numbers w(2; 3, t) Abstract In this paper we present results and conjectures on the van der Waerden numbers w(2; 3, t). We have computed the exact value of the previously unknown van der Waerden number w(2; 3, 19) = 349, and we provide new lower bounds for t = 30, we conjecture these bounds to be exact. The lower bounds for w(2; 3, t)(More)