A coloring of the leaves of a tree T is called convex, if it is possible to give each internal node a color, such that for each color, the set of nodes with that color forms a subtree of T . Motivated by a problem from phylogenetic reconstruction, we study the problem, when given a tree with a coloring of its leaves, to recolor as few as possible leaves to obtain a convex coloring. We present f...

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...

For a mixed hypergraphH= (X,C,D), where C andD are set systems over the vertex set X, a coloring is a partition of X into ‘color classes’such that everyC ∈ Cmeets some class in more than one vertex, and everyD ∈ D has a nonempty intersection with at least two classes.A vertex-order x1, x2, . . . , xn onX (n=|X|) is uniquely colorable if the subhypergraph induced by {xj : 1 j i} has precisely on...

Given a weighted undirected graph G and a nonnegative integer k, the maximum k-star colorable subgraph problem consists of finding an induced subgraph of G which has maximum weight and can be star colored with at most k colors; a star coloring does not color adjacent nodes with the same color and avoids coloring any 4-path with exactly two colors. In this article, we investigate the polyhedral ...

We prove that if G and H are primitive strongly regular graphs with the same parameters and φ is a homomorphism from G to H, then φ is either an isomorphism or a coloring (homomorphism to a complete subgraph). Moreover, any such coloring is optimal for G and its image is a maximum clique of H. Therefore, the only endomorphisms of a primitive strongly regular graph are automorphisms or colorings...

The problem of computing good graph colorings arises in many diverse applications , such as in the estimation of sparse Jacobians and in the development of eecient, parallel iterative methods for solving sparse linear systems. In this paper we present an asynchronous graph coloring heuristic well suited to distributed memory parallel computers. We present experimental results obtained on an Int...

We present a method for solving the independent set formulation of the graph coloring problem (where there is one variable for each independent set in the graph). We use a column generation method for implicit optimization of the linear program at each node of the branch-and-bound tree. This approach, while requiring the solution of a diicult subproblem as well as needing sophisticated branchin...

The k-Coloring problem is to test whether a graph can be colored with at most k colors such that no two adjacent vertices receive the same color. If a graph G does not contain a graph H as an induced subgraph, then G is called H-free. For any fixed graph H on at most 6 vertices, it is known that 3-Coloring is polynomial-time solvable on H-free graphs whenever H is a linear forest and NP-complet...

In studying the scalability of optical networks, one problem which arises involves coloring the vertices of the n-cube with as few colors as possible such that any two vertices whose Hamming distance is at most k are colored differently. Determining the exact value of χk̄(n), the minimum number of colors needed, appears to be a difficult problem. In this note, we improve the known lower and uppe...

In this work we develop a new quadratic placement technique where we prematurely abort the linear system solver to save runtime. This has low impact in the placement flow due to the expand-contract phenomena intrinsic to the ICCG solver outlined in this paper. A coloring scheme for placement useful for comparing visually placement results is described. The coloring scheme then is used to create...