PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2007 | 27 | 2 | 313-321
Tytuł artykułu

On θ-graphs of partial cubes

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The Θ-graph Θ(G) of a partial cube G is the intersection graph of the equivalence classes of the Djoković-Winkler relation. Θ-graphs that are 2-connected, trees, or complete graphs are characterized. In particular, Θ(G) is complete if and only if G can be obtained from K₁ by a sequence of (newly introduced) dense expansions. Θ-graphs are also compared with familiar concepts of crossing graphs and τ-graphs.
Wydawca
Rocznik
Tom
27
Numer
2
Strony
313-321
Opis fizyczny
Daty
wydano
2007
otrzymano
2006-04-25
poprawiono
2006-12-28
zaakceptowano
2006-12-28
Twórcy
  • Department of Mathematics and Computer Science, FNM, University of Maribor, Gosposvetska 84, 2000 Maribor, Slovenia
autor
  • Institute of Mathematics, Physics and Mechanics, Gosposvetska 84, 2000 Maribor, Slovenia
Bibliografia
  • [1] B. Bresar, Coloring of the Θ-graph of a median graph, Problem 2005.3, Maribor Graph Theory Problems. http://www-mat.pfmb.uni-mb.si/personal/klavzar/MGTP/index.html.
  • [2] B. Bresar, W. Imrich and S. Klavžar, Tree-like isometric subgraphs of hypercubes, Discuss. Math. Graph Theory 23 (2003) 227-240, doi: 10.7151/dmgt.1199.
  • [3] B. Bresar and S. Klavžar, Crossing graphs as joins of graphs and Cartesian products of median graphs, SIAM J. Discrete Math. 21 (2007) 26-32, doi: 10.1137/050622997.
  • [4] B. Bresar and T. Kraner Sumenjak, Θ-graphs of partial cubes and strong edge colorings, Ars Combin., to appear.
  • [5] V.D. Chepoi, d-Convexity and isometric subgraphs of Hamming graphs, Cybernetics 1 (1988) 6-9, doi: 10.1007/BF01069520.
  • [6] M.M. Deza and M. Laurent, Geometry of cuts and metrics, Algorithms and Combinatorics, 15 (Springer-Verlag, Berlin, 1997).
  • [7] D. Djoković, Distance preserving subgraphs of hypercubes, J. Combin. Theory (B) 14 (1973) 263-267, doi: 10.1016/0095-8956(73)90010-5.
  • [8] R.J. Faudree, A. Gyarfas, R.H. Schelp and Z. Tuza, Induced matchings in bipartite graphs, Discrete Math. 78 (1989) 83-87, doi: 10.1016/0012-365X(89)90163-5.
  • [9] W. Imrich and S. Klavžar, A convexity lemma and expansion procedures for bipartite graphs, European J. Combin. 19 (1998) 677-685, doi: 10.1006/eujc.1998.0229.
  • [10] W. Imrich and S. Klavžar, Product Graphs: Structure and Recognition (Wiley, New York, 2000).
  • [11] S. Klavžar and M. Kovse, Partial cubes and their τ-graphs, European J. Combin. 28 (2007) 1037-1042.
  • [12] S. Klavžar and H.M. Mulder, Partial cubes and crossing graphs, SIAM J. Discrete Math. 15 (2002) 235-251, doi: 10.1137/S0895480101383202.
  • [13] F.R. McMorris, H.M. Mulder and F.R. Roberts, The median procedure on median graphs, Discrete Appl. Math. 84 (1998) 165-181, doi: 10.1016/S0166-218X(98)00003-1.
  • [14] H.M. Mulder, The structure of median graphs, Discrete Math. 24 (1978) 197-204, doi: 10.1016/0012-365X(78)90199-1.
  • [15] H.M. Mulder, The Interval Function of a Graph (Math. Centre Tracts 132, Mathematisch Centrum, Amsterdam, 1980).
  • [16] M. van de Vel, Theory of Convex Structures (North-Holland, Amsterdam, 1993).
  • [17] A. Vesel, Characterization of resonance graphs of catacondensed hexagonal graphs, MATCH Commun. Math. Comput. Chem. 53 (2005) 195-208.
  • [18] P. Winkler, Isometric embeddings in products of complete graphs, Discrete Appl. Math. 7 (1984) 221-225, doi: 10.1016/0166-218X(84)90069-6.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1363
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.