# Some applications of pq-groups in graph theory

Discussiones Mathematicae Graph Theory (2004)

- Volume: 24, Issue: 1, page 109-114
- ISSN: 2083-5892

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topGeoffrey Exoo. "Some applications of pq-groups in graph theory." Discussiones Mathematicae Graph Theory 24.1 (2004): 109-114. <http://eudml.org/doc/270670>.

@article{GeoffreyExoo2004,

abstract = {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.},

author = {Geoffrey Exoo},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {Ramsey number; edge coloring; cage; degree; girth; Cayley graph},

language = {eng},

number = {1},

pages = {109-114},

title = {Some applications of pq-groups in graph theory},

url = {http://eudml.org/doc/270670},

volume = {24},

year = {2004},

}

TY - JOUR

AU - Geoffrey Exoo

TI - Some applications of pq-groups in graph theory

JO - Discussiones Mathematicae Graph Theory

PY - 2004

VL - 24

IS - 1

SP - 109

EP - 114

AB - 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.

LA - eng

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

UR - http://eudml.org/doc/270670

ER -

## References

top- [1] G. Exoo, Some New Ramsey Colorings, Electronic J. Combinatorics 5 (1998) #R29. Zbl0896.05043
- [2] G. Exoo, A Small Trivalent Graph of Girth 14, to appear. Zbl0985.05040
- [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.

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