# Altitude of wheels and wheel-like graphs

Open Mathematics (2010)

• Volume: 8, Issue: 2, page 319-326
• ISSN: 2391-5455

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## Abstract

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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.

## How to cite

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Tomasz Dzido, and Hanna Furmańczyk. "Altitude of wheels and wheel-like graphs." Open Mathematics 8.2 (2010): 319-326. <http://eudml.org/doc/269750>.

@article{TomaszDzido2010,
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.},
author = {Tomasz Dzido, Hanna Furmańczyk},
journal = {Open Mathematics},
keywords = {Altitude; Edge-ordering; Increasing paths; altitude; edge-ordering; increasing paths},
language = {eng},
number = {2},
pages = {319-326},
title = {Altitude of wheels and wheel-like graphs},
url = {http://eudml.org/doc/269750},
volume = {8},
year = {2010},
}

TY - JOUR
AU - Tomasz Dzido
AU - Hanna Furmańczyk
TI - Altitude of wheels and wheel-like graphs
JO - Open Mathematics
PY - 2010
VL - 8
IS - 2
SP - 319
EP - 326
AB - 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.
LA - eng
KW - Altitude; Edge-ordering; Increasing paths; altitude; edge-ordering; increasing paths
UR - http://eudml.org/doc/269750
ER -

## References

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1. [1] Brandstädt A., Le V.B., Spinrad J.P., Graph Classes: A Survey, Philadelphia, PA: SIAM, 1987 Zbl0919.05001
2. [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 Zbl1080.05046
3. [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.2005.02.007 Zbl1062.05131
4. [4] Chvátal V., Komlós J., Some combinatorial theorems on monotonicity,Canad. Math. Bull., 1971, 14,151–157 Zbl0214.23503
5. [5] Cockayne E.J., Mynhardt C.M., Altitude of K 3,n , J. Combin. Math. Combin. Comp., 2005, 52, 143–157
6. [6] Katrenič J., Semanišin G., Complexity of ascent finding problem, Proceedings of SOFSEM 2008, High Tatras, Slovakia, January 20–24, 2008, II, 70–77

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