Modular and Lexical Matchings in the Middle Levels Graph Open Access
Wingfield, Kevin (2012)
Abstract
Abstract
Modular and Lexical Matchings in the Middle Levels Graph
Classes of explicitly defined matchings in the middle levels
bipartite graph
induced by the Boolean lattice are investigated. The original
motivation for
an investigation into the Hamiltonicity of the middle levels
bipartite graph
came from the conjecture of Havel. Here, we collect some known
results
and present some new observations that indicate that, when
disjoint, the
2-factors obtained from taking the union of pairs of these
matchings always
contain short cycles.
Table of Contents
Contents
1 Introduction 1
1.1 Definitions and notation ..................... 4
1.2 Automorphisms in Bk ............................ 6
2 Modular Matchings 7
2.1 Definitions and preliminaries................... 7
2.2 Pairwiseunionsofmodularmatchings. . . . . . . . . . . . . . 10
2.3 3-factors of modular matchings ................. 16
3 Lexical Matchings 20
3.1 Definitions and background results ............... 21
3.2 Partial results........................... 27
4 Future Work 33
Bibliography 35
About this Master's Thesis
School | |
---|---|
Department | |
Degree | |
Submission | |
Language |
|
Research Field | |
Keyword | |
Committee Chair / Thesis Advisor | |
Committee Members |
Primary PDF
Thumbnail | Title | Date Uploaded | Actions |
---|---|---|---|
Modular and Lexical Matchings in the Middle Levels Graph () | 2018-08-28 16:31:39 -0400 |
|
Supplemental Files
Thumbnail | Title | Date Uploaded | Actions |
---|