نتایج جستجو برای: vertex decomposable

تعداد نتایج: 41901  

Journal: :Theor. Comput. Sci. 2001
Van Bang Le Bert Randerath

We answer a question of Brandstädt et al. by showing that deciding whether a line graph with maximum degree 5 has a stable cutset is NP -complete. Conversely, the existence of a stable cutset in a line graph with maximum degree at most 4 can be decided efficiently. The proof of our NP -completeness result is based on a refinement on a result due to Chvátal that recognizing decomposable graphs w...

Journal: :Discrete Mathematics 2000
Sonoko Moriyama Fumihiko Takeuchi

We give new examples of shellable but not extendably shellable two dimensional simplicial complexes. They include minimal examples, which are smaller than those previously known. We also give examples of shellable but not vertex decomposable two dimensional simplicial complexes. Among them are extendably shellable ones. This shows that neither extendable shellability nor vertex decomposability ...

2012
NICOLAI HÄHNLE VINCENT PILAUD

Provan and Billera introduced notions of (weak) decomposability of simplicial complexes as a means of attempting to prove polynomial upper bounds on the diameter of the facet-ridge graph of a simplicial polytope. Recently, De Loera and Klee provided the first examples of simplicial polytopes that are not weakly vertex-decomposable. These polytopes are polar to certain simple transportation poly...

Journal: :J. Comb. Theory, Ser. A 2011
Satoshi Murai

In 1992, Thomas Bier introduced a surprisingly simply way to construct a large number of simplicial spheres. He proved that, for any simplicial complex ∆ on the vertex set V with ∆ 6= 2 , the deleted join of ∆ with its Alexander dual ∆∨ is a combinatorial sphere. In this paper, we extend Bier’s construction to multicomplexes, and study their combinatorial and algebraic properties. We show that ...

Journal: :Discrete Applied Mathematics 2002
Dominique Barth Olivier Baudon Joël Puech

In this article, we deal with graphs modelling interconnection networks of parallel systems (parallel computers, networks of workstations,..). We want to share the nodes of such a network between many users, each one needing a given number of nodes. Thus, a graph G with N vertices is said to be decomposable if for each set fn 1 We show that determining if a given tripode (three disjoint chains ...

2007
Saieed Akbari Allen Herman

We say that two graphs G and H with the same vertex set commute if their adjacency matrices commute. In this article, we show that for any natural number r, the complete multigraphK n is decomposable into commuting perfect matchings if and only if n is a 2-power. Also, it is shown that the complete graph Kn is decomposable into commuting Hamilton cycles if and only if n is a prime number. © 200...

2014
AMIR MOUSIVAND SEYED AMIN SEYED FAKHARI SIAMAK YASSEMI Seyed Fakhari

Let G be a finite simple graph on a vertex set V (G) = {x11, . . . , xn1}. Also let m1, . . . , ,mn ≥ 2 be integers and G1, . . . , Gn be connected simple graphs on the vertex sets V (Gi) = {xi1, . . . , ximi}. In this paper, we provide necessary and sufficient conditions on G1, . . . , Gn for which the graph obtained by attaching the Gi to G is unmixed or vertex decomposable. Then we character...

2009
ADAM VAN TUYL

Let G be a bipartite graph with edge ideal I(G) whose quotient ring R/I(G) is sequentially Cohen-Macaulay. We prove: (1) the independence complex of G must be vertex decomposable, and (2) the Castelnuovo-Mumford regularity of R/I(G) can be determined from the invariants of G.

Journal: :Discrete & Computational Geometry 2013
Michal Lason

We prove that if a pure simplicial complex of dimension d with n facets has the least possible number of (d − 1)-dimensional faces among all complexes with n faces of dimension d, then it is vertex decomposable. This answers a question of J. Herzog and T. Hibi. In fact, we prove a generalization of their theorem using combinatorial methods.

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