Carl Yerger

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We exhibit an explicit list of nine graphs such that a graph drawn in the Klein bottle is 5-colorable if and only if it has no subgraph isomorphic to a member of the list. 31 August 2007, revised 18 January 2012. Partially supported by NSF under Grant No. DMS-0200595. Partially supported by NSF under Grants No. DMS-0200595, DMS-0354742, and DMS-0701077.(More)
Let [a, b] denote the integers between a and b inclusive and, for a finite subset X ⊆ Z, let diam (X) = max(X) − min(X). We write X <p Y provided max(X) < min(Y ). For a positive integer m, let f(m,m,m; 2) be the least integer N such that any 2-coloring ∆ : [1, N ] → {0, 1} has three monochromatic m-sets B1, B2, B3 ⊆ [1, N ] (not necessarily of the same(More)
Given a configuration of pebbles on the vertices of a connected graph G, a pebbling move is defined as the removal of two pebbles from some vertex and the placement of one of these on an adjacent vertex. The pebbling number of a graph G is the smallest integer k such that for each vertex v and each configuration of k pebbles on G there is a sequence of(More)
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