The main result of this paper is a coefficient formula that sharpens and generalizes Alon and Tarsiâ€™s Combinatorial Nullstellensatz. On its own, it is a result about polynomials, providing someâ€¦ (More)

We study the list coloring number of k-uniform k-partite hypergraphs. Answering a question of Ramamurthi and West, we present a new upper bound which generalizes Alon and Tarsiâ€™s bound for bipartiteâ€¦ (More)

We introduce a coloring game on graphs, in which each vertex v of a graph G owns a stack of lvâˆ’1 erasers. In each round of this game the first player Mr. Paint takes an unused color, and colors someâ€¦ (More)

We extend results about critically k-colorable graphs to choosability and paintability (list colorability and on-line list colorability). Using a strong version of Brooksâ€™ Theorem, we generalizeâ€¦ (More)

We present a purely combinatorial proof of Alon and Tarsiâ€™s Theorem about list colorings and orientations of graphs. More precisely, we describe a winning strategy for Mrs. Correct in theâ€¦ (More)

We introduce colorings and orientations of matrices as generalizations of the graph theoretic terms. The permanent per(A[Î¶|Î¾]) of certain copies A[Î¶|Î¾] of a matrix A can be expressed as a weightedâ€¦ (More)

We work with a unifying linear algebra formulation for nowhere-zero flows and colorings of graphs and matrices. Given a subspace (code) U â‰¤ Zk n â€“ e.g. the bond or the cycle space over Zk of anâ€¦ (More)

We prove that the list-chromatic index and paintability index of K6 is 5. That indeed Ï‡ â€² l(K6) = 5 was a still open special case of the List Coloring Conjecture. Our proof demonstrates howâ€¦ (More)