Minimal vertex separators of chordal graphs
نویسندگان
چکیده
منابع مشابه
Minimal vertex separators and new characterizations for dually chordal graphs
Many works related to dually chordal graphs, their cliques and neighborhoods were published. We will undertake a similar study but by considering minimal separators and their properties. Moreover we find new characterizations of dually chordal graphs.
متن کاملGraphs with complete minimal k-vertex separators
G. A. Dirac characterized chordal graphs as those in which minimal vertex separators always induce complete subgraphs. I generalize a traditional (2-)vertex separator to a k-vertex separator — meaning a set S of vertices whose removal puts k independent vertices into k separate components. Generalizing Dirac’s theorem, the {P5, 2P3}-free chordal graphs are the graphs in which minimal k-separato...
متن کاملOn minimal vertex separators of dually chordal graphs: Properties and characterizations
Many works related to dually chordal graphs, their cliques and neighborhoods were published [1, 6]. We will undertake a similar study by considering minimal vertex separators and their properties instead. We find a necessary and sufficient condition for every minimal vertex separator to be contained in the closed neighborhood of a vertex and two major characterizations of dually chordal graphs ...
متن کاملComplement 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.
متن کاملVertex partitions of chordal graphs
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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 1998
ISSN: 0166-218X
DOI: 10.1016/s0166-218x(98)00123-1