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2003 | 23 | 2 | 215-225
Tytuł artykułu

Arboreal structure and regular graphs of median-like classes

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We consider classes of graphs that enjoy the following properties: they are closed for gated subgraphs, gated amalgamation and Cartesian products, and for any gated subgraph the inverse of the gate function maps vertices to gated subsets. We prove that any graph of such a class contains a peripheral subgraph which is a Cartesian product of two graphs: a gated subgraph of the graph and a prime graph minus a vertex. Therefore, these graphs admit a peripheral elimination procedure which is a generalization of analogous procedure in median graphs. We characterize regular graphs of these classes whenever they enjoy an additional property. As a corollary we derive that regular weakly median graphs are precisely Cartesian products in which each factor is a complete graph or a hyperoctahedron.
Słowa kluczowe
Wydawca
Rocznik
Tom
23
Numer
2
Strony
215-225
Opis fizyczny
Daty
wydano
2003
otrzymano
2001-09-26
poprawiono
2002-02-06
Twórcy
  • University of Maribor, FERI, Smetanova 17, 2000 Maribor, Slovenia
Bibliografia
  • [1] R.P. Anstee and M. Farber, On bridged graphs and cop-win graphs, J. Combin. Theory (B) 44 (1988) 22-28, doi: 10.1016/0095-8956(88)90093-7.
  • [2] H.-J. Bandelt and V. Chepoi, Decomposition and l₁-embedding of weakly median graphs, European J. Combin. 21 (2000) 701-714, doi: 10.1006/eujc.1999.0377.
  • [3] H.-J. Bandelt and H.M. Mulder, Regular pseudo-median graphs, J. Graph Theory 4 (1988) 533-549, doi: 10.1002/jgt.3190120410.
  • [4] H.-J. Bandelt and H.M. Mulder, Pseudo-median graphs: decomposition via amalgamation and Cartesian multiplication, Discrete Math. 94 (1991) 161-180, doi: 10.1016/0012-365X(91)90022-T.
  • [5] H.-J. Bandelt, H.M. Mulder and E. Wilkeit, Quasi-median graphs and algebras, J. Graph Theory 18 (1994) 681-703, doi: 10.1002/jgt.3190180705.
  • [6] A. Brandstaet, V.B. Le and J.P. Spinrad, Graphs classes: A survey (SIAM, Philadelphia, 1999), doi: 10.1137/1.9780898719796.
  • [7] B. Brešar, On the natural imprint function of a graph, European J. Combin. 23 (2002) 149-161, doi: 10.1006/eujc.2001.0555.
  • [8] M. Chastand, Fiber-complemented graphs, I. Structure and invariant subgraphs, Discrete Math. 226 (2001) 107-141, doi: 10.1016/S0012-365X(00)00183-7.
  • [9] W. Imrich and S. Klavžar, Product graphs: Structure and recognition (Wiley, New York, 2000).
  • [10] S. Klavžar and H.M. Mulder, Median graphs: characterizations, location theory and related structures, J. Combin. Math. Combin. Comp. 30 (1999) 103-127.
  • [11] H.M. Mulder, The structure of median graphs, Discrete Math. 24 (1978) 197-204, doi: 10.1016/0012-365X(78)90199-1.
  • [12] H.M. Mulder, The Interval Function of a Graph, Mathematical Centre Tracts 132 (Mathematisch Centrum, Amsterdam, 1980).
  • [13] H.M. Mulder, The expansion procedure for graphs, in: R. Bodendiek ed., Contemporary Methods in Graph Theory (B.I.-Wissenschaftsverlag, Manhaim/Wien/Zürich, 1990) 459-477.
  • [14] C. Tardif, Prefibers and the Cartesian product of metric spaces, Discrete Math. 109 (1992) 283-288, doi: 10.1016/0012-365X(92)90298-T.
  • [15] M.L.J. van de Vel, Theory of convex structures (North Holland, Amsterdam, 1993).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1198
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