Showing papers by "Richard A. Brualdi published in 2006"
TL;DR: This paper determines the sum choice number of K2,n, and shows that every tree on n vertices can be obtained from Kn by consecutively deleting single edges where all intermediate graphs are sc-greedy.
Abstract: Let G=(V,E) be a graph with n vertices and e edges. The sum choice number of G is the smallest integer p such that there exist list sizes (f(v):v ∈ V) whose sum is p for which G has a proper coloring no matter which color lists of size f(v) are assigned to the vertices v. The sum choice number is bounded above by n+e. If the sum choice number of G equals n+e, then G is sum choice greedy. Complete graphs Kn are sum choice greedy as are trees. Based on a simple, but powerful, lemma we show that a graph each of whose blocks is sum choice greedy is also sum choice greedy. We also determine the sum choice number of K2,n, and we show that every tree on n vertices can be obtained from Kn by consecutively deleting single edges where all intermediate graphs are sc-greedy.
35 citations
TL;DR: Using a Ryser-like algorithm, canonical constructions are given for matrices in A(R,S) whose insertion tableaux have shape @l=S and R^*, respectively.
31 citations
01 Aug 2006
3 citations
01 Aug 2006
1 citations
TL;DR: B bipartite graphs G and G' are characterized which are related by a matching preserver and the matching preservers between them, and a bijection $\psi: E (G) \rightarrow E(G')$ is called a (perfect) matching preservative.
Abstract: For two bipartite graphs $G$ and $G'$, a bijection $\psi: E(G) \rightarrow E(G')$ is called a (perfect) matching preserver provided that $M$ is a perfect matching in $G$ if and only if $\psi(M)$ is a perfect matching in $G'$. We characterize bipartite graphs $G$ and $G'$ which are related by a matching preserver and the matching preservers between them.