Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Open Mathematics

formerly Central European Journal of Mathematics

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

IMPACT FACTOR 2018: 0.726
5-year IMPACT FACTOR: 0.869

CiteScore 2018: 0.90

SCImago Journal Rank (SJR) 2018: 0.323
Source Normalized Impact per Paper (SNIP) 2018: 0.821

Mathematical Citation Quotient (MCQ) 2018: 0.34

ICV 2018: 152.31

Open Access
See all formats and pricing
More options …
Volume 8, Issue 2


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


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

  • [1] Brandstädt A., Le V.B., Spinrad J.P., Graph Classes: A Survey, Philadelphia, PA: SIAM, 1987 Google Scholar

  • [2] Burger A.P., Cockayne E.J., Mynhardt C.M., Altitude of small complete and complete bipartite graphs, Australas. J. Combin., 2005, 31, 167–177 Google Scholar

  • [3] Burger A.P., Mynhardt C.M., Clark T.C., Falvai B., Henderson N.D.R., Altitude of regular graphs with girth at least five,Disc. Math.,2005,294,241–257 http://dx.doi.org/10.1016/j.disc.2005.02.007CrossrefGoogle Scholar

  • [4] Chvátal V., Komlós J., Some combinatorial theorems on monotonicity,Canad. Math. Bull., 1971, 14,151–157 CrossrefGoogle Scholar

  • [5] Cockayne E.J., Mynhardt C.M., Altitude of K 3,n , J. Combin. Math. Combin. Comp., 2005, 52, 143–157 Google Scholar

  • [6] Katrenič J., Semanišin G., Complexity of ascent finding problem, Proceedings of SOFSEM 2008, High Tatras, Slovakia, January 20–24, 2008, II, 70–77 Google Scholar

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.

Export Citation

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

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

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

Comments (0)

Please log in or register to comment.
Log in