Constructing vertex decomposable graphs
Authors
Abstract:
Recently, some techniques such as adding whiskers and attaching graphs to vertices of a given graph, have been proposed for constructing a new vertex decomposable graph. In this paper, we present a new method for constructing vertex decomposable graphs. Then we use this construction to generalize the result due to Cook and Nagel.
similar resources
constructing vertex decomposable graphs
recently, some techniques such as adding whiskers and attaching graphs to vertices of a given graph, have been proposed for constructing a new vertex decomposable graph. in this paper, we present a new method for constructing vertex decomposable graphs. then we use this construction to generalize the result due to cook and nagel.
full textDense Arbitrarily Vertex Decomposable Graphs
A graph G of order n is said to be arbitrarily vertex decomposable if for each sequence (n1, . . . , nk) of positive integers such that n1 + · · · + nk = n there exists a partition (V1, . . . , Vk) of the vertex set of G such that for each i ∈ {1, . . . , k}, Vi induces a connected subgraph of G on ni vertices. The main result of the paper reads as follows. Suppose that G is a connected graph o...
full textRecursively arbitrarily vertex-decomposable graphs
A graph G = (V,E) is arbitrarily vertex decomposable if for any sequence τ of positive integers adding up to |V |, there is a sequence of vertex-disjoint subsets of V whose orders are given by τ , and which induce connected graphs. The main aim of this paper is to study the recursive version of this problem. We present a solution for trees, suns, and partially for a class of 2-connected graphs ...
full textVertex Decomposable Simplicial Complexes Associated to Path Graphs
Introduction Vertex decomposability of a simplicial complex is a combinatorial topological concept which is related to the algebraic properties of the Stanley-Reisner ring of the simplicial complex. This notion was first defined by Provan and Billera in 1980 for k-decomposable pure complexes which is known as vertex decomposable when . Later Bjorner and Wachs extended this concept to non-pure ...
full textVertex Decomposable Graphs and Obstructions to Shellability
Inspired by several recent papers on the edge ideal of a graph G, we study the equivalent notion of the independence complex of G. Using the tool of vertex decomposability from geometric combinatorics, we show that 5-chordal graphs with no chordless 4-cycles are shellable and sequentially Cohen-Macaulay. We use this result to characterize the obstructions to shellability in flag complexes, exte...
full textA note on arbitrarily vertex decomposable graphs
A graph G of order n is said to be arbitrarily vertex decomposable if for each sequence (n1, ..., nk) of positive integers such that n1 + ... + nk = n there exists a partition (V1, ..., Vk) of the vertex set of G such that for each i ∈ {1, ..., k}, Vi induces a connected subgraph of G on ni vertices. In this paper we show that if G is a two-connected graph on n vertices with the independence nu...
full textMy Resources
Journal title
volume 42 issue 4
pages 809- 817
publication date 2016-08-01
By following a journal you will be notified via email when a new issue of this journal is published.
Hosted on Doprax cloud platform doprax.com
copyright © 2015-2023