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The endomorphism type of certain bipartite graphs and a characterization of projective planes

Ralf Köhl (né Gramlich), Katja Möser and Hendrik Van Maldeghem (UGent)
(2013) GRAPHS AND COMBINATORICS. 29(2). p.253-257
Author
Organization
Abstract
Fan (in Southeast Asian Bull Math 25, 217-221, 2001) determines the endomorphism type of a finite projective plane. In this note we show that Fan's result actually characterizes the class of projective planes among the finite bipartite graphs of diameter three. In fact, this will follow from a generalization of Fan's theorem and its converse to all finite bipartite graphs with diameter d and girth g such that (1) d + 1 < ga parts per thousand currency sign2d, and (2) every pair of adjacent edges is contained in a circuit of length g.
Keywords
Projective plane, Generalized polygon, Bipartite graph, Endomorphism type

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MLA
Köhl (né Gramlich), Ralf, et al. “The Endomorphism Type of Certain Bipartite Graphs and a Characterization of Projective Planes.” GRAPHS AND COMBINATORICS, vol. 29, no. 2, 2013, pp. 253–57, doi:10.1007/s00373-011-1110-6.
APA
Köhl (né Gramlich), R., Möser, K., & Van Maldeghem, H. (2013). The endomorphism type of certain bipartite graphs and a characterization of projective planes. GRAPHS AND COMBINATORICS, 29(2), 253–257. https://doi.org/10.1007/s00373-011-1110-6
Chicago author-date
Köhl (né Gramlich), Ralf, Katja Möser, and Hendrik Van Maldeghem. 2013. “The Endomorphism Type of Certain Bipartite Graphs and a Characterization of Projective Planes.” GRAPHS AND COMBINATORICS 29 (2): 253–57. https://doi.org/10.1007/s00373-011-1110-6.
Chicago author-date (all authors)
Köhl (né Gramlich), Ralf, Katja Möser, and Hendrik Van Maldeghem. 2013. “The Endomorphism Type of Certain Bipartite Graphs and a Characterization of Projective Planes.” GRAPHS AND COMBINATORICS 29 (2): 253–257. doi:10.1007/s00373-011-1110-6.
Vancouver
1.
Köhl (né Gramlich) R, Möser K, Van Maldeghem H. The endomorphism type of certain bipartite graphs and a characterization of projective planes. GRAPHS AND COMBINATORICS. 2013;29(2):253–7.
IEEE
[1]
R. Köhl (né Gramlich), K. Möser, and H. Van Maldeghem, “The endomorphism type of certain bipartite graphs and a characterization of projective planes,” GRAPHS AND COMBINATORICS, vol. 29, no. 2, pp. 253–257, 2013.
@article{6834619,
  abstract     = {{Fan (in Southeast Asian Bull Math 25, 217-221, 2001) determines the endomorphism type of a finite projective plane. In this note we show that Fan's result actually characterizes the class of projective planes among the finite bipartite graphs of diameter three. In fact, this will follow from a generalization of Fan's theorem and its converse to all finite bipartite graphs with diameter d and girth g such that (1) d + 1 < ga parts per thousand currency sign2d, and (2) every pair of adjacent edges is contained in a circuit of length g.}},
  author       = {{Köhl (né Gramlich), Ralf and Möser, Katja and Van Maldeghem, Hendrik}},
  issn         = {{0911-0119}},
  journal      = {{GRAPHS AND COMBINATORICS}},
  keywords     = {{Projective plane,Generalized polygon,Bipartite graph,Endomorphism type}},
  language     = {{eng}},
  number       = {{2}},
  pages        = {{253--257}},
  title        = {{The endomorphism type of certain bipartite graphs and a characterization of projective planes}},
  url          = {{http://doi.org/10.1007/s00373-011-1110-6}},
  volume       = {{29}},
  year         = {{2013}},
}
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