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Winning An Independence Achievement Game., Mark C. Taylor

Electronic Theses and Dissertations

The game "Generalized Kayles (or Independence Achievement)" is played by two players A and B on an arbitrary graph G. The players alternate removing a vertex and its neighbors from G, the winner being the last player with a nonempty set from which to choose. In this thesis, we present winning strategies for some paths.

Sandwich Theorem And Calculation Of The Theta Function For Several Graphs, Marcia Ling Riddle

Theses and Dissertations

This paper includes some basic ideas about the computation of a function theta(G), the theta number of a graph G, which is known as the Lovasz number of G. theta(G^c) lies between two hard-to-compute graph numbers omega(G), the size of the largest lique in a graph G, and chi(G), the minimum number of colors need to properly color the vertices of G. Lovasz and Grotschel called this the "Sandwich Theorem". Donald E. Knuth gives four additional definitions of theta, theta_1, theta_2, theta_3, theta_4 and proves that they are all equal.

First I am going to describe the proof of the …

Bounding The Number Of Graphs Containing Very Long Induced Paths, Steven Kay Butler

Theses and Dissertations

Induced graphs are used to describe the structure of a graph, one such type of induced graph that has been studied are long paths.

In this thesis we show a way to represent such graphs in terms of an array with two colors and a labeled graph. Using this representation and the techniques of Polya counting we will then be able to get upper and lower bounds for graphs containing a long path as an induced subgraph.

In particular, if we let P(n,k) be the number of graphs on n+k vertices which contains P_n, a path on n vertices, as …

The Embedding Of Complete Bipartite Graphs Onto Grids With A Minimum Grid Cutwidth, Mário Rocha

Theses Digitization Project

Algorithms will be domonstrated for how to embed complete bipartite graphs onto 2xn type grids, where the imimum grid cutwidth is attained.