Complement of Special Chordal Graphs and Vertex Decomposability
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Abstract:
In this paper, we introduce a subclass of chordal graphs which contains $d$-trees and show that their complement are vertex decomposable and so is shellable and sequentially Cohen-Macaulay.
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complement of special chordal graphs and vertex decomposability
in this paper, we introduce a subclass of chordal graphs which contains $d$-trees and show that their complement are vertex decomposable and so is shellable and sequentially cohen-macaulay.
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A k-tree is a chordal graph with no (k + 2)-clique. An l-treepartition of a graph G is a vertex partition of G into ‘bags’, such that contracting each bag to a single vertex gives an l-tree (after deleting loops and replacing parallel edges by a single edge). We prove that for all k ≥ l ≥ 0, every k-tree has an l-tree-partition in which every bag induces a connected ⌊k/(l + 1)⌋-tree. An analogo...
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full textVertex Deletion Problems on Chordal Graphs
Containing many classic optimization problems, the family of vertex deletion problems has an important position in algorithm and complexity study. The celebrated result of Lewis and Yannakakis gives a complete dichotomy of their complexity. It however has nothing to say about the case when the input graph is also special. This paper initiates a systematic study of vertex deletion problems from ...
full textSubset feedback vertex sets in chordal graphs
Given a graph G = (V, E) and a set S ⊆ V , a set U ⊆ V is a subset feedback vertex set of (G, S ) if no cycle in G[V \ U] contains a vertex of S . The Subset Feedback Vertex Set problem takes as input G, S , and an integer k, and the question is whether (G, S ) has a subset feedback vertex set of cardinality or weight at most k. Both the weighted and the unweighted versions of this problem are ...
full textReconfiguration graphs for vertex colourings of chordal and chordal bipartite graphs
A k-colouring of a graph G = (V,E) is a mapping c : V → {1, 2, . . . , k} such that c(u) 6= c(v) whenever uv is an edge. The reconfiguration graph of the k-colourings of G contains as its vertex set the k-colourings of G, and two colourings are joined by an edge if they differ in colour on just one vertex of G. We introduce a class of k-colourable graphs, which we call k-colour-dense graphs. We...
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Journal title
volume 39 issue 4
pages 619- 625
publication date 2013-09-01
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