Sarah K. Merz

The Domination and Competition Graphs of a Tournament

The matching graph M(G) of a graph G is that graph whose vertices are the maximum matchings in G and where two vertices M1 and M2 of M(G) are adjacent if and only if |M1 - M2| = 1. When M(G) is connected, this graph models a metric space whose metric is defined on the set of maximum matchings in G. Which graphs are matching graphs of some graph is not known in general. We determine several forbidden induced subgraphs of matching graphs and add even cycles to the list of known matching graphs. In another direction, we study the behavior of sequences of iterated matching graphs.

Competition Graphs of Strongly Connected and Hamiltonian Digraphs

A radio communication network can be modeled by a digraph,

Domination Graphs with Nontrivial Components

D

Chromatic numbers of competition graphs

, where there is an arc from vertex

A Characterization of Graphs With Interval Two-Step Graphs

x

Domination Graphs of Tournaments and Digraphs

to vertex

Domination Graphs of Tournaments with Isolated Vertices.

y

A Characterization of Graphs With Interval Squares

if a signal sent from

The (1,2)-step competition graph of a tournament

x

The Competition Graphs of Interval Digraphs

can be received at