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Maximal Cliques in Graphs Associated with Combinatorial Systems


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.


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
Funding AgencyGrant Number
Bohnenblust Travel FundUNSPECIFIED
Record Number:CaltechTHESIS:05172018-100953589
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:10908
Deposited By: Mel Ray
Deposited On:29 Jun 2018 15:28
Last Modified:19 Apr 2021 22:27

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