Paths in graphs

B. Bollobás; A. Sarkar

doi:10.1556/sscmath.38.2001.1-4.8

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Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 38: Issue 1-4

Paths in graphs

Authors:

B. Bollobás

B. Bollobás Please ask the editor of the journal.

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A. Sarkar

A. Sarkar Technical Physics and Prototype Engineering Division, Bhabha, Atomic Research Centre Mumbai 400 085, India

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Pages:: 115–137

Online Publication Date:: 22 Jul 2005

Publication Date:: 01 May 2001

Article Category:: Journal Article

DOI:: https://doi.org/10.1556/sscmath.38.2001.1-4.8

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We prove that if 2 2 then the number of paths of length three in a graphGof size m is at most 2m(m - k)(k - 2)=k. Equality is attained if G is the union of Kk and isolated vertices. We also give asymptotically best possible bounds for the maximal number of paths of length s, for arbitrary s, in graphs of size m. Lastly,we discuss the more general problem of maximizing the number of subgraphs isomorphic to a given graph H in graphs of size m.

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Studia Scientiarum Mathematicarum Hungarica

Print ISSN:: 0081-6906

Online ISSN:: 1588-2896

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Gábor SIMONYI (Rényi Institute of Mathematics)
András STIPSICZ (Rényi Institute of Mathematics)
Géza TÓTH (Rényi Institute of Mathematics)

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Imre BÁRÁNY (Rényi Institute of Mathematics)
Károly BÖRÖCZKY (Rényi Institute of Mathematics and Central European University)
Péter CSIKVÁRI (ELTE, Budapest)
Joshua GREENE (Boston College)
Penny HAXELL (University of Waterloo)
Andreas HOLMSEN (Korea Advanced Institute of Science and Technology)
Ron HOLZMAN (Technion, Haifa)
Satoru IWATA (University of Tokyo)
Tibor JORDÁN (ELTE, Budapest)
Roy MESHULAM (Technion, Haifa)
Frédéric MEUNIER (École des Ponts ParisTech)
Márton NASZÓDI (ELTE, Budapest)
Eran NEVO (Hebrew University of Jerusalem)
János PACH (Rényi Institute of Mathematics)
Péter Pál PACH (BME, Budapest)
Andrew SUK (University of California, San Diego)
Zoltán SZABÓ (Princeton University)
Martin TANCER (Charles University, Prague)
Gábor TARDOS (Rényi Institute of Mathematics)
Paul WOLLAN (University of Rome "La Sapienza")

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Rank by Impact Factor	Q3 (Mathematics)
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Studia Scientiarum Mathematicarum Hungarica
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ISSN	0081-6906 (Print)
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