Altitude of wheels and wheel-like graphs

Tomasz Dzido 1  and Hanna Furmańczyk 1
  • 1 University of Gdańsk


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.

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