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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Vespri, Vincenzo / Marano, Salvatore Angelo


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Open Access
Online
ISSN
2391-5455
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Volume 8, Issue 2

Issues

Volume 13 (2015)

Altitude of wheels and wheel-like graphs

Tomasz Dzido / Hanna Furmańczyk
Published Online: 2010-04-14 | DOI: https://doi.org/10.2478/s11533-010-0017-4

Abstract

An edge-ordering of a graph G=(V, E) is a one-to-one mapping f:E(G)→{1, 2, ..., |E(G)|}. A path of length k in G is called a (k, f)-ascent if f increases along the successive edges forming the path. The altitude α(G) of G is the greatest integer k such that for all edge-orderings f, G has a (k, f)-ascent.

In our paper we give exact values of α(G) for all helms and wheels. Furthermore, we use our result to obtain altitude for graphs that are subgraphs of helms.

MSC: 05C78

Keywords: Altitude; Edge-ordering; Increasing paths

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About the article

Published Online: 2010-04-14

Published in Print: 2010-04-01


Citation Information: Open Mathematics, Volume 8, Issue 2, Pages 319–326, ISSN (Online) 2391-5455, DOI: https://doi.org/10.2478/s11533-010-0017-4.

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© 2010 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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[1]
J. Katrenič and G. Semanišin
Discrete Applied Mathematics, 2010, Volume 158, Number 15, Page 1624

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