Turán numbers for odd wheels

Tomasz Dzido; Andrzej Jastrzębski

doi:10.1016/j.disc.2017.10.003

Turán numbers for odd wheels

Abstract

The Turán number ex(n,G) is the maximum number of edges in any n-vertex graph that does not contain a subgraph isomorphic to G. A wheel W_n is a graph on n vertices obtained from a C_{n−1} by adding one vertex w and making w adjacent to all vertices of the C_{n−1}. We obtain two exact values for small wheels: ex(n,W_5)=\lfloor n^2/4+n/2\rfloor, ex(n,W_7)=\lfloor n^2/4+n/2+1 \rfloor. Given that ex(n,W_6) is already known, this paper completes the spectrum for all wheels up to 7 vertices. In addition, we present the construction which gives us the lower bound ex(n,W_{2k+1})>\lfloor n^2/4 \rfloor + \lfloor n/2 \rfloor in general case.

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Authors (2)

Tomasz Dzido dr hab.
- UG
Andrzej Jastrzębski mgr inż.

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Publication version: Accepted or Published Version
DOI:: Digital Object Identifier (open in new tab) 10.1016/j.disc.2017.10.003
License: Copyright (2017 Elsevier B.V)

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Category:: Articles
Type:: artykuł w czasopiśmie wyróżnionym w JCR
Published in:: DISCRETE MATHEMATICS no. 341, edition 4, pages 1150 - 1154,
ISSN: 0012-365X
Language:: English
Publication year:: 2018
Bibliographic description:: Dzido T., Jastrzębski A.: Turán numbers for odd wheels// DISCRETE MATHEMATICS. -Vol. 341, iss. 4 (2018), s.1150-1154
DOI:: Digital Object Identifier (open in new tab) 10.1016/j.disc.2017.10.003
Verified by:: Gdańsk University of Technology