Two Counterexamples in Graph Drawing

Authors:
Ondrej Sýkora;László A. Székely;Imrich Vrto
Affiliations:
-;-;-
Venue:
WG '02 Revised Papers from the 28th International Workshop on Graph-Theoretic Concepts in Computer Science
Year:
2002

Citing 4
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Abstract

We provide counterexamples to two conjectures known in the field of graph drawing. The first conjecture (made by J. Halton ten years ago) asserts that the thickness of any graph of maximum degree 驴 is at most 驴(驴+2)/4驴. We give an existence proof that there are graphs of the thickness 驴驴/2驴--this is known to be the best possible upper bound. The second conjecture (made by F. Shahrokhi recently) proposes a relation between the crossing number of a graph and the optimal linear arrangement of that graph. We construct a graph which does not satisfy this relation.