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On the Number of 4-Edge Paths in Graphs With Given Edge Density

Part of: Graph theory

Published online by Cambridge University Press:  23 December 2016

DÁNIEL T. NAGY
DÁNIEL T. NAGY*
Affiliation:
Eötvös Loránd University, Egyetem tér 1-3, Budapest 1053, Hungary (e-mail: dani.t.nagy@gmail.com)
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Abstract

We investigate the number of 4-edge paths in graphs with a given number of vertices and edges, proving an asymptotically sharp upper bound on this number. The extremal construction is the quasi-star or the quasi-clique graph, depending on the edge density. An easy lower bound is also proved. This answer resembles the classic theorem of Ahlswede and Katona about the maximal number of 2-edge paths, and a recent theorem of Kenyon, Radin, Ren and Sadun about k-edge stars.

MSC classification

Primary: 05C35: Extremal problems
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 26 , Issue 3 , May 2017 , pp. 431 - 447
Copyright
Copyright © Cambridge University Press 2016 

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References

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