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2015

Sizes of the extremal girth 5 graphs of orders from 40 to 49

Backelin, Jörgen

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The Tur\'an type numbers for graphs without 3-cycles and 4-cycles are determined for vertex numbers from 40 to 49 inclusive.

Hence, now, 43 of the first 50 numbers of OEIS A006856 are known.
Estimates for the remaining seven numbers are presented.

Sizes of the extremal girth 5 graphs of orders from 40 to 49 · Around

Built on

A. J. Hoffman and R. R. Singleton, On Moore graphs with diameters 2 and 3
1960
Earlier work this paper cites.
R. K. Guy, A problem of Zarankiewicz
1968
Earlier work this paper cites.
M. O’Keefe, P.-K. Wong, A smallest graph of girth 5 and valency 6
1979
Earlier work this paper cites.

Similar

P.-K. Wong, On the uniqueness of the smallest graphs of girth 5 and valency 6
Original
1979
Cited alongside, same era.
R. D. Dutton, R. C. Brigham Edges in graphs with large girth
1991
Cited alongside, same era.
D. K. Garnick and N. A. Nieuwejaar, Non-isomorphic extremal graphs without three-cycles or four-cycles
1992
Cited alongside, same era.
Item A006856
Cited in the paper.
Item A159847
Cited in the paper.

Then

D. K. Garnick, Y. H. Kwong, and F. Lazebnik, Extremal graphs without three-cycles or four-cycles
1993
Later among the works it cites.
M. Codish, A. Miller, P. Prosser, P. J. Stuckey, Breaking symmetries in graph representation
2013
Later among the works it cites.

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