FMF, Mathematical Library, Lj. (MAKLJ)
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A theorem about a contractible and light edgeDvořák, Zdeněk ; Škrekovski, RisteLeta 1955 je Kotzig pokazal, da vsak ravninski 3-povezan graf vsebuje povezavo stopnje ▫$\le 13$▫. Če pa graf ne vsebuje točke stopnje 3, imamo povezavo stopnje ▫$\le 11$▫. Taki povezavi rečemo lahka ... povezava. Pomemben rezultat Steinitza pravi, da so skeleti konveksnih 3-politopov natanko 3-povezani ravninski grafi. Po drugi strani pa je leta 1961 Tuttle dokazal, da vsak 3-povezan graf vsebuje skrčljivo povezavo. V članku izboljšamo Kotzigov izrek, tako da pokažemo, da vsak tak graf, različen od ▫$K_4$▫, vsebuje povezavo, ki je hkrati lahka in skrčljiva. Kot posledico dobimo, da se da vsak konveksni 3-politop konstruirati iz tetraedra s sekvečno ekspanzijo točk stopnje največ 11.Source: SIAM journal on discrete mathematics. - ISSN 0895-4801 (Vol. 20, no. 1, 2006, str. 55-61)Type of material - article, component partPublish date - 2006Language - englishCOBISS.SI-ID - 14249305
Author
Dvořák, Zdeněk |
Škrekovski, Riste
Topics
matematika |
teorija grafov |
politop |
lahka povezava |
skrčljiva povezava |
3-povezani grafi |
ravninski grafi |
mathematics |
graph theory |
polytope |
light edge |
contractible edge |
3-connected graphs |
planar garphs
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Dvořák, Zdeněk | ![]() |
Škrekovski, Riste | 15518 |
Source: Personal bibliographies
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