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2003 | 23 | 2 | 227-240
Tytuł artykułu

Tree-like isometric subgraphs of hypercubes

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Tree-like isometric subgraphs of hypercubes, or tree-like partial cubes as we shall call them, are a generalization of median graphs. Just as median graphs they capture numerous properties of trees, but may contain larger classes of graphs that may be easier to recognize than the class of median graphs. We investigate the structure of tree-like partial cubes, characterize them, and provide examples of similarities with trees and median graphs. For instance, we show that the cube graph of a tree-like partial cube is dismantlable. This in particular implies that every tree-like partial cube G contains a cube that is invariant under every automorphism of G. We also show that weak retractions preserve tree-like partial cubes, which in turn implies that every contraction of a tree-like partial cube fixes a cube. The paper ends with several Frucht-type results and a list of open problems.
Wydawca
Rocznik
Tom
23
Numer
2
Strony
227-240
Opis fizyczny
Daty
wydano
2003
otrzymano
2002-01-09
poprawiono
2002-06-11
Twórcy
  • University of Maribor, FERI, Smetanova 17, 2000 Maribor, Slovenia
  • Montanuniversität Leoben, A-8700 Leoben, Austria
  • Department of Mathematics, PEF, University of Maribor, Koroska cesta 160, 2000 Maribor, Slovenia
Bibliografia
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Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1199
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