Transversals of Longest Paths and Cycles
Identifieur interne : 001744 ( Main/Exploration ); précédent : 001743; suivant : 001745Transversals of Longest Paths and Cycles
Auteurs : Dieter Rautenbach [Allemagne] ; Jean-Sébastien Sereni [France]Source :
Descripteurs français
- mix :
Abstract
Let G be a graph of order n. Let lpt(G) be the minimum cardinality of a set X of vertices of G such that X intersects every longest path of G and define lct(G) analogously for cycles instead of paths. We prove that (i) lpt(G) ≤ ceiling(n/4-n^{2/3}/90), if G is connected, (ii) lct(G) ≤ ceiling(n/3-n^{2/3}/36), if G is 2-connected, and (iii) lpt(G) ≤ 3, if G is a connected circular arc graph. Our bound on lct(G) improves an earlier result of Thomassen and our bound for circular arc graphs relates to an earlier statement of Balister et al. the argument of which contains a gap. Furthermore, we prove upper bounds on lpt(G) for planar graphs and graphs of bounded tree-width.
Url:
Affiliations:
- Allemagne, France
- Bade-Wurtemberg, District de Tübingen, Grand Est, Lorraine (région)
- Metz, Nancy, Ulm
- Université d'Ulm, Université de Lorraine
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Le document en format XML
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Let lpt(G) be the minimum cardinality of a set X of vertices of G such that X intersects every longest path of G and define lct(G) analogously for cycles instead of paths. We prove that (i) lpt(G) ≤ ceiling(n/4-n^{2/3}/90), if G is connected, (ii) lct(G) ≤ ceiling(n/3-n^{2/3}/36), if G is 2-connected, and (iii) lpt(G) ≤ 3, if G is a connected circular arc graph. Our bound on lct(G) improves an earlier result of Thomassen and our bound for circular arc graphs relates to an earlier statement of Balister et al. the argument of which contains a gap. Furthermore, we prove upper bounds on lpt(G) for planar graphs and graphs of bounded tree-width.</div></front></TEI><affiliations><list><country><li>Allemagne</li><li>France</li></country><region><li>Bade-Wurtemberg</li><li>District de Tübingen</li><li>Grand Est</li><li>Lorraine (région)</li></region><settlement><li>Metz</li><li>Nancy</li><li>Ulm</li></settlement><orgName><li>Université d'Ulm</li><li>Université de Lorraine</li></orgName></list><tree><country name="Allemagne"><region name="Bade-Wurtemberg"><name sortKey="Rautenbach, Dieter" sort="Rautenbach, Dieter" uniqKey="Rautenbach D" first="Dieter" last="Rautenbach">Dieter Rautenbach</name></region></country><country name="France"><region name="Grand Est"><name sortKey="Sereni, Jean Sebastien" sort="Sereni, Jean Sebastien" uniqKey="Sereni J" first="Jean-Sébastien" last="Sereni">Jean-Sébastien Sereni</name></region></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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