The Maximum Number of Paths of Length Three in a Planar Graph

Ervin Győri; Addisu Paulos; Nika Salia; Casey Tompkins; Oscar Zamora

doi:10.1007/978-3-030-83823-2_41

The Maximum Number of Paths of Length Three in a Planar Graph

Ervin Győri
, Addisu Paulos^*
, Nika Salia
, Casey Tompkins
, Oscar Zamora

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

1 Scopus citations

Abstract

Let f(n, H) denote the maximum number of copies of H possible in an n-vertex planar graph. The function f(n, H) has been determined when H is a cycle of length 3 or 4 by Hakimi and Schmeichel and when H is a complete bipartite graph with smaller part of size 1 or 2 by Alon and Caro. We determine f(n, H) exactly in the case when H is a path of length 3.

Original language	English
Title of host publication	Trends in Mathematics
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	262-266
Number of pages	5
DOIs	https://doi.org/10.1007/978-3-030-83823-2_41
State	Published - 2021
Externally published	Yes

Publication series

Name	Trends in Mathematics
Volume	14
ISSN (Print)	2297-0215
ISSN (Electronic)	2297-024X

Bibliographical note

Publisher Copyright:
© 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Keywords

Apollonian networks
Maximal planar graph
Planar graph

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/978-3-030-83823-2_41

Cite this

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AU - Salia, Nika

AU - Tompkins, Casey

AU - Zamora, Oscar

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