Treffer: Bounds for graphs of given girth and generalized polygons
Title:
Bounds for graphs of given girth and generalized polygons
Authors:
Publisher Information:
Lugansk Taras Shevchenko National University, Lugansk, 2019.
Publication Year:
2019
Subject Terms:
Extremal problems in graph theory, Transportation, logistics and supply chain management, tactical configuration, Extremal combinatorics, bipartite graph, Random graphs (graph-theoretic aspects), extremal graph theory, Group actions on designs, etc, 0102 computer and information sciences, Probabilistic methods in extremal combinatorics, including polynomial methods (combinatorial Nullstellensatz, etc.), family of graphs of high girth, 01 natural sciences, operations research
Document Type:
Fachzeitschrift
Article
File Description:
application/xml
Accession Number:
edsair.dedup.wf.002..4b10dd29220e59210912e27cca98f4d8
Database:
OpenAIRE
Weitere Informationen
The authors propose an upper bound on the number of edges for bipartite graphs with average bidegrees \(\eta\) and \(\xi\) satisfying the inequality \(\eta \geq \xi^m\) for a real number \(m>1\). Lower bounds for the numbers of points and lines of tactical configurations in terms of their bidegrees are presented. The authors prove also that finite generalized polygons have the smallest possible order among tactical configurations of given bidegrees and girth. Finally, an upper bound on the size of graphs of girth \(g \geq 2t-1\) is established.