Batch scheduling of conflicting jobs is modeled by batch coloring of a graph. Given an undirected graph and the number of colors required by each vertex, we need to find a proper batch coloring of the graph, namely, to partition the vertices to batches which are independent sets and assign to each batch a contiguous set of colors, whose size is equal to the maximum color requirement of any vert...

The problem of online coloring an unknown graph is known to be hard. Here we consider the problem of online coloring in the relaxed situation where the input must be isomorphic to a given known graph. All that foils a computationally powerful player is that it is not known to which sections of the graph the vertices to be colored belong. We show that the performance ratio of any online coloring...

For planar graphs, we consider the problems of list edge coloring and list total coloring. Edge coloring is the problem of coloring the edges while ensuring that two edges that are adjacent receive different colors. Total coloring is the problem of coloring the edges and the vertices while ensuring that two edges that are adjacent, two vertices that are adjacent, or a vertex and an edge that ar...

Motivated by the definition of linear coloring on simplicial complexes, recently introduced in the context of algebraic topology, and the framework through which it was studied, we introduce the colinear coloring on graphs. We provide an upper bound for the chromatic number χ(G), for any graph G, and show that G can be colinearly colored in polynomial time by proposing a simple algorithm. The c...

Processor cache memory management is a challenging issue as it deeply impact performances and power consumption of electronic devices. It has been shown that allocating data structures to memory for a given application (as MPEG encoding, filtering or any other signal processing application) can be modeled as a minimum k-weighted graph coloring problem, on the so-called conflict graph. The graph...

In a graph G, a vertex is said to dominate itself and all its neighbors. A dominating set of a graph G is a subset of vertices that dominates every vertex of G. The domination number γ(G) is the minimum cardinality of a dominating set of G. A proper coloring of a graph G is a function from the set of vertices of the graph to a set of colors such that any two adjacent vertices have different col...