On a Lower Bound for Short Noncontractible Cycles in Embedded Graphs
In this paper, a technique is developed that allows the construction of a triangulation of a closed orientable surface of genus $g$ by an $n$-vertex graph in such a way that the triangulation does not have short noncontractible cycles. Using this technique, a counterexample is constructed to a conje...
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| Veröffentlicht in: | SIAM journal on discrete mathematics 1990-05, Vol.3 (2), p.281-293 |
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| creator | Przytycka, T. Przytycki, J. H. |
| description | In this paper, a technique is developed that allows the construction of a triangulation of a closed orientable surface of genus $g$ by an $n$-vertex graph in such a way that the triangulation does not have short noncontractible cycles. Using this technique, a counterexample is constructed to a conjecture by Hutchinson that the length of the shortest noncontractible cycle in any such triangulation is $O(\sqrt{n/g} )$. The presented technique can also be used to show that the function $\sqrt{n/g} \log^{ *} g$ provides a lower bound for the shortest noncontractible cycle in a triangulation of a surface of genus $g$. |
| doi_str_mv | 10.1137/0403024 |
| format | Article |
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| identifier | ISSN: 0895-4801 |
| ispartof | SIAM journal on discrete mathematics, 1990-05, Vol.3 (2), p.281-293 |
| issn | 0895-4801 1095-7146 |
| language | eng |
| recordid | cdi_proquest_journals_925631818 |
| source | LOCUS - SIAM's Online Journal Archive |
| subjects | Algebra |
| title | On a Lower Bound for Short Noncontractible Cycles in Embedded Graphs |
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