Publication

Online Coloring of Comparability Graphs: some results

Benjamin Leroy-Beaulieu
2007
Reports

Abstract

We study online partitioning of posets from a graph theoretical point of view, which is coloring and cocoloring in comparability graphs. For the coloring problem, we analyse the First-Fit algorithm and show a ratio of $O(\sqrt{n})$ ; furthermore, we devise an algorithm with a competitivity ratio of $\frac{\chi+1}{2}$ . For the cocoloring problem, we point out a tight bound of $\frac{n}{4} + \frac{1}{2}$ and we give better bounds in some more restricted cocoloring problems.

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Benjamin Leroy-Beaulieu
2007
Reports

Abstract

Official source

Related concepts (32)

Graph coloring

In graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints. In its simplest form, it is a way of coloring the vertices of a graph such that no two adjacent vertices are of the same color; this is called a vertex coloring. Similarly, an edge coloring assigns a color to each edge so that no two adjacent edges are of the same color, and a face coloring of a planar graph assigns a color to each face or region so that no two faces that share a boundary have the same color.

Edge coloring

In graph theory, a proper edge coloring of a graph is an assignment of "colors" to the edges of the graph so that no two incident edges have the same color. For example, the figure to the right shows an edge coloring of a graph by the colors red, blue, and green. Edge colorings are one of several different types of graph coloring. The edge-coloring problem asks whether it is possible to color the edges of a given graph using at most k different colors, for a given value of k, or with the fewest possible colors.

Comparability graph

In graph theory, a comparability graph is an undirected graph that connects pairs of elements that are comparable to each other in a partial order. Comparability graphs have also been called transitively orientable graphs, partially orderable graphs, containment graphs, and divisor graphs. An incomparability graph is an undirected graph that connects pairs of elements that are not comparable to each other in a partial order.

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Online Coloring of Comparability Graphs: some results

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