Geir Agnarsson

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We give nontrivial bounds for the inductiveness or degeneracy of power graphs Gk of a planar graph G. This implies bounds for the chromatic number as well, since the inductiveness naturally relates to a greedy algorithm for vertex-coloring the given graph. The inductiveness moreover yields bounds for the choosability of the graph. We show that the(More)
The k-th power of a graph G is a graph on the same vertex set as G, where a pair of vertices is connected by an edge if they are of distance at most k in G. We study the structure of powers of chordal graphs and the complexity of coloring them. We start by giving new and constructive proofs of the known facts that any power of an interval graph is an(More)
A strong vertex coloring of a hypergraph assigns distinct colors to vertices that are contained in a common hyperedge. This captures many previously studied graph coloring problems. We present nearly tight upper and lower bound on approximating general hypergraphs, both offline and online. We then consider various parameters that make coloring easier, and(More)
This paper deals with approximations of maximum independent sets in non-uniform hypergraphs of low degree. We obtain the first performance ratio that is sublinear in terms of the maximum or average degree of the hypergraph. We extend this to the weighted case and give a O(D̄ log log D̄/ log D̄) bound, where D̄ is the average weighted degree in a hypergraph,(More)
With a nite graph G V E we associate a partially ordered set P X P with X V E and x e in P if and only if x is an endpoint of e in G This poset is called the incidence poset of G In this paper we consider the function M p d de ned for p d as the maximum number of edges a graph G can have when it has p vertices and the dimension of its incidence poset is at(More)
A queue-based Prüfer-like code is used to determine the expected number of level-i nodes in a random labeled tree on n nodes. Level-1 nodes are the leaves of a given tree and level-i nodes are leaves after all nodes in levels 1 through (i-1) have been deleted. More precisely, we study the expected fraction f(i) of n nodes that are in levels 1 through i.(More)
Abstract. Call the set S1 × · · · × St t–dimensional m–box if |Si| = m for every i = 1, . . . , t. Let Rt(m, r) be the smallest integer R such that for every r–coloring of t–fold cartesian product of [R] one can find a monochromatic t–dimensional m–box. We give a lower and an upper bound for Rt(m, r). We also consider the discrepancy problem connected to(More)
Graph labeling is a classic problem in mathematics and computing. In this paper we study an interesting set of graph labeling problems which were first introduced by Kantabutra (2007). The general problem, here called the graph relabeling problem, is to take an undirected graph G=(V, E), two labelings l<sub>1</sub> and l<sub>2</sub> of G, and a label(More)