INTEGERS: ELECTRONIC JOURNAL OF COMBINATORIAL NUMBER THEORY 7 (2007), #A29 DISJUNCTIVE RADO NUMBERS FOR x1 + x2 + c = x3

Given two equations E1 and E2, the disjunctive Rado number for E1 and E2 is the least integer n, provided that it exists, such that for every coloring of the set {1, 2,..., n} with two colors there exists a monochromatic solution to either E1 or E2. If no such integer n exists, then the disjunctive Rado number for E1 and E2 is infinite. Let R(c, k) represen

New proofs for strongly chordal graphs and chordal bipartite graphs

We give new proofs of well-known characterizations of strongly chordal graphs and chordal bipartite graphs. The key ingredient is the dual hypertree structure for totally balanced hypergraphs. We also consider split graphs and threshold graphs