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- Geir Agnarsson, MagnÃºs M. HalldÃ³rsson
- SODA
- 2000

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 theâ€¦ (More)

- Geir Agnarsson, Raymond Greenlawy
- 2000

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 anâ€¦ (More)

- Geir Agnarsson, MagnÃºs M. HalldÃ³rsson
- WAOA
- 2004

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, andâ€¦ (More)

Let n be a nonnegative integer, and let Ã£ = (a1, . . . , ak) be a k-tuple of positive integers. The term denumerant, introduced by Sylvester, denotes the number D(n; Ã£) of ways one can partition the number n into parts a1, . . . , ak. In this article we use direct combinatorial methods to find concrete and simply expressible upper and lower bounds for D(n;â€¦ (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(DÌ„ log log DÌ„/ log DÌ„) bound, where DÌ„ is the average weighted degree in a hypergraph,â€¦ (More)

- Geir Agnarsson, Stefan Felsner, William T. Trotter
- Discrete Mathematics
- 1999

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 atâ€¦ (More)

A queue-based PrÃ¼fer-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.â€¦ (More)

- Geir Agnarsson, MagnÃºs M. HalldÃ³rsson
- SODA
- 2004

We investigate the clique number, the chromatic number and the inductiveness (or the degeneracy) of the square <i>G</i><sup>2</sup> of an outerplanar graph <i>G</i>, and bound as a function of the maximum degree Δ of <i>G</i>. Our main result is a tight bound of Δ for the inductiveness of the square of any outerplanar graph <i>G</i>, when Δâ€¦ (More)

- Geir Agnarsson, Benjamin Doerr, Tomasz Schoen
- Discrete Mathematics
- 2001

Abstract. Call the set S1 Ã— Â· Â· Â· Ã— St tâ€“dimensional mâ€“box if |Si| = m for every i = 1, . . . , t. Let Rt(m, r) be the smallest integer R such that for every râ€“coloring of tâ€“fold cartesian product of [R] one can find a monochromatic tâ€“dimensional mâ€“box. We give a lower and an upper bound for Rt(m, r). We also consider the discrepancy problem connected toâ€¦ (More)

- Geir Agnarsson, Ray Greenlaw, Sanpawat Kantabutra
- 2008 5th International Conference on Electricalâ€¦
- 2008

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 labelâ€¦ (More)