Some applications of pq-groups in graph theory

• Autorzy: Geoffrey Exoo
• Języki publikacji: EN

Abstrakty

EN

We describe some new applications of nonabelian pq-groups to construction problems in Graph Theory. The constructions include the smallest known trivalent graph of girth 17, the smallest known regular graphs of girth five for several degrees, along with four edge colorings of complete graphs that improve lower bounds on classical Ramsey numbers.

Słowa kluczowe

EN

Ramsey number; edge coloring; cage; degree; girth; Cayley graph

Kategorie tematyczne

• 05C25: Graphs and abstract algebra (groups, rings, fields, etc.)
• 05C35: Extremal problems
• 05C55: Generalized Ramsey theory

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2004
• Tom: 24
• Numer: 1
• Strony: 109-114

Daty

wydano

2004

otrzymano

2002-02-04

poprawiono

2002-08-28

Twórcy

autor

Geoffrey Exoo

• Department of Mathematics and Computer Science, Indiana State University, Terre Haute, IN 47809, USA

Bibliografia

• [1] G. Exoo, Some New Ramsey Colorings, Electronic J. Combinatorics 5 (1998) #R29.
• [2] G. Exoo, A Small Trivalent Graph of Girth 14, to appear.
• [3] M. Hall, The Theory of Groups (The Macmillan Company, New York, 1959).
• [4] S.P. Radziszowski, Small Ramsey Numbers, Dynamic Survey DS1, Electronic J. Combinatorics 1 (1994) pp. 28.
• [5] G. Royle, Cubic Cages, http://www.cs.uwa.edu.au/~gordon/cages/index.html, February, 2001 (Accessed: January 20, 2002).
• [6] M. Schönert et al, Groups, Algorithms and Programming, version 4 release 2, Department of Mathematics, University of Western Australia.

Identyfikatory

DOI

10.7151/dmgt.1217