Geir Agnarsson

Coloring Powers of Planar Graphs

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 inductiveness of a square of a planar graph G is at most

Recognition of matrix rings II

\lceil 9\Delta /5 \rceil

The maximum number of edges in a graph of bounded dimension, with applications to ring theory

, for the maximum degree

Strong colorings of hypergraphs

\Delta

The number of outside corners of monomial ideals

sufficiently large, and that it is sharp. In general, we show for a fixed integer

SDP-Based Algorithms for Maximum Independent Set Problems on Hypergraphs

k\geq1

SDP-based algorithms for maximum independent set problems on hypergraphs

the inductiveness, the chromatic number, and the choosability of Gk to be

On the number of hypercubic bipartitions of an integer

O(\Delta^{\lfloor k/2 \rfloor})

The graph relabeling problem and its variants

, which is tight.

Note: Strongly simplicial vertices of powers of trees

This paper provides several new criteria for a ring to be a complete matrix ring. Some applications demonstrate their efficacy; and their relative strengths are indicated by calculating the structures they impose on universal algebras.