CaltechTHESIS
  A Caltech Library Service

Maximal Cliques in Graphs Associated with Combinatorial Systems

Citation

Rands, Bruce Michael Ian (1982) Maximal Cliques in Graphs Associated with Combinatorial Systems. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/e1b1-vd02. https://resolver.caltech.edu/CaltechTHESIS:05172018-100953589

Abstract

Maximal cliques in various graphs with combinatorial significance are investigated. The Erdös, Ko, Rado theorem, concerning maximal sets of blocks, pairwise intersecting in s points, is extended to arbitrary t-designs, and a new proof of the theorem is given thereby.

The simplest case of this phenomenon is dealt with in detail, namely cliques of size r in the block graphs of Steiner systems S(2,k,v). Following this, the possibility of nonunique geometrisation of such block graphs is considered, and a nonexistence proof in one case is given, when the alternative geometrising cliques are normal.

A new Association Scheme is introduced for the 1-factors of the complete graph; its eigenvalues are calcu1ated using the Representation Theory of the Symmetric Group, and various applications are found, concerning maximal cliques in the scheme.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Mathematics
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Wilson, Richard M.
Thesis Committee:
  • Dilworth, Robert P. (chair)
  • Kechris, Alexander S.
  • Ryser, Herbert J.
  • Wales, David B.
  • Wilson, Richard M.
Defense Date:25 May 1982
Funders:
Funding AgencyGrant Number
Bohnenblust Travel FundUNSPECIFIED
Record Number:CaltechTHESIS:05172018-100953589
Persistent URL:https://resolver.caltech.edu/CaltechTHESIS:05172018-100953589
DOI:10.7907/e1b1-vd02
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:10908
Collection:CaltechTHESIS
Deposited By: Melissa Ray
Deposited On:29 Jun 2018 15:28
Last Modified:19 Apr 2021 22:27

Thesis Files

[img]
Preview
PDF - Final Version
See Usage Policy.

24MB

Repository Staff Only: item control page