A k-list-assignment for a graph G assigns to each vertex v of G a list L(v) of admissible colors , where |L(v)| ≥ k. A graph is k-list-colorable (or k-choosable) if it can be properly colored from the lists for every k-listassignment. We prove the following conjecture posed by Thomassen in 1994: “There are only finitely many listcolor-critical graphs with all lists of cardinality at least 5 on ...

The long-standing Erd\H{o}s-Faber-Lov\'asz conjecture states that every $n$-uniform linear hypergaph with $n$ edges has a proper vertex-coloring using colors. In this paper we propose an algebraic framework to the problem and formulate corresponding stronger conjecture. Using Combinatorial Nullstellensatz, reduce existence of non-zero coefficients in certain polynomials. These are turn related ...

Ž Many combinatorial problems can be efficiently solved for partial k-trees graphs . of treewidth bounded by k . The edge-coloring problem is one of the well-known combinatorial problems for which no efficient algorithms were previously known, except a polynomial-time algorithm of very high complexity. This paper gives a linear-time sequential algorithm and an optimal parallel algorithm which f...

As register allocation is one of the most important phases in optimizing compilers, much work has been done to improve its quality and speed. We present a novel register allocation architecture for programs in SSA-form which simplifies register allocation significantly. We investigate certain properties of SSA-programs and their interference graphs, showing that they belong to the class of chor...

A vertex coloring of a simplicial complex ∆ is called a linear coloring if it satisfies the property that for every pair of facets (F1, F2) of ∆, there exists no pair of vertices (v1, v2) with the same color such that v1 ∈ F1\F2 and v2 ∈ F2\F1. We show that every simplicial complex ∆ which is linearly colored with k colors includes a subcomplex ∆ with k vertices such that ∆ is a strong deformat...

A coloring of a tree is convex if the vertices that pertain to any color induce a connected subtree; a partial coloring (which assigns colors to some of the vertices) is convex if it can be completed to a convex (total) coloring. Convex coloring of trees arises in areas such as phylogenetics, linguistics, etc. eg, a perfect phylogenetic tree is one in which the states of each character induce a...

Defective coloring is a variant of traditional vertex-coloring, according to which adjacent vertices are allowed to have the same color, as long as the monochromatic components induced by the corresponding edges have a certain structure. Due to its important applications, as for example in the bipartisation of graphs, this type of coloring has been extensively studied, mainly with respect to th...

Many well-known combinatorial optimization problems can be stated over the set of acyclic orientations of an undirected graph. For example, acyclic orientations with certain diameter constraints are closely related to the optimal solutions of the vertex coloring and frequency assignment problems. In this paper we introduce a linear programming formulation of acyclic orientations with path const...

Finding a good graph coloring quickly is often a crucial phase in the development of efficient, parallel algorithms for many scientific and engineering applications. In this paper we consider the problem of solving the graph coloring problem itself in parallel. We present a simple and fast parallel graph coloring heuristic that is well suited for shared memory programming and yields an almost l...