Dually Chordal Graphs
نویسندگان
چکیده
Recently in several papers, graphs with maximum neighborhood orderings were characterized and turned out to be algorithmically useful. This paper gives a unified framework for characterizations of those graphs in terms of neighborhood and clique hypergraphs which have the Helly property and whose line graph is chordal. These graphs are dual (in the sense of hypergraphs) to chordal graphs. By using the hypergraph approach in a systematical way new results are obtained, some of the old results are generalized, and some of the proofs are simplified.
منابع مشابه
Total-Chromatic Number and Chromatic Index of Dually Chordal Graphs
A graph is dually chordal if it is the clique graph of a chordal graph. Alternatively, a graph is dually chordal if it admits a maximum neighbourhood order. This class generalizes known subclasses of chordal graphs such as doubly chordal graphs, strongly chordal graphs and interval graphs. We prove that Vizing's total-colour conjecture holds for dually chordal graphs. We describe a new heuristi...
متن کاملMinimal 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 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 کاملDetermining possible sets of leaves for spanning trees of dually chordal graphs
It will be proved that the problem of determining whether a set of vertices of a dually chordal graphs is the set of leaves of a tree compatible with it can be solved in polynomial time by establishing a connection with finding clique trees of chordal graphs with minimum number of leaves.
متن کامل3-Colourability of Dually Chordal Graphs in Linear Time
A graph G is dually chordal if there is a spanning tree T of G such that any maximal clique of G induces a subtree in T . This paper investigates the Colourability problem on dually chordal graphs. It will show that it is NP-complete in case of four colours and solvable in linear time with a simple algorithm in case of three colours. In addition, it will be shown that a dually chordal graph is ...
متن کاملThe Algorithmic Use of Hypertree Structure and Maximum Neighbourhood Orderings
Thl.: use of (generalized) tree structure in graphs is one of the main topics in the field of eflicient graph algorithms. The well-known partial k-tree (resp. treewidth) approach belongs to this kind of research and bases on a tree structure of constant-size bounded maximal cliques. Without size bound on the cliques this tree structure of maximal cliques characterizes chordal graphs which are k...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- SIAM J. Discrete Math.
دوره 11 شماره
صفحات -
تاریخ انتشار 1993