Polynomial-Time Algorithm for the Leafage of Chordal Graphs
نویسندگان
چکیده
Every chordal graph G can be represented as the intersection graph of a collection of subtrees of a host tree, the so-called tree model of G. The leafage l(G) of a connected chordal graph G is the minimum number of leaves of the host tree of a tree model of G. This concept was first defined by I.-J. Lin, T.A. McKee, and D.B. West in [9]. In this contribution, we present the first polynomial time algorithm for computing l(G) for a given chordal graph G. In fact, our algorithm runs in time O(n) and it also constructs a tree model of G whose host tree has l(G) leaves.
منابع مشابه
The vertex leafage of chordal graphs
Every chordal graph G can be represented as the intersection graph of a collection of subtrees of a host tree, a so-called tree model of G. The leafage l(G) of a connected chordal graph G is the minimum number of leaves of the host tree of a tree model of G and the vertex leafage vl(G) is the smallest number k such that there exists a tree model of G in which every subtree has at most k leaves....
متن کاملThe leafage of a chordal graph
The leafage l(G) of a chordal graph G is the minimum number of leaves of a tree in which G has an intersection representation by subtrees. We obtain upper and lower bounds on l(G) and compute it on special classes. The maximum of l(G) on n-vertex graphs is n − lg n− 1 2 lg lg n+O(1). The proper leafage l(G) is the minimum number of leaves when no subtree may contain another; we obtain upper and...
متن کاملLinear Algorithms for Chordal Graphs of Bounded Directed Vertex Leafage
The directed vertex leafage of a chordal graph G is the smallest integer k such that G is the intersection graph of subtrees of a rooted directed tree where each subtree has at most k leaves. In this note, we show how to find in time O(kn) an optimal colouring, a maximum independent set, a maximum clique, and an optimal clique cover of an n-vertex chordal graph G with directed vertex leafage k ...
متن کاملCapturing Logarithmic Space and Polynomial Time on Chordal Claw-Free Graphs
We show that the class of chordal claw-free graphs admits LREC=-definable canonization. LREC= is a logic that extends first-order logic with counting by an operator that allows it to formalize a limited form of recursion. This operator can be evaluated in logarithmic space. It follows that there exists a logarithmic-space canonization algorithm, and therefore a logarithmic-space isomorphism tes...
متن کاملThe Existence of Homeomorphic Subgraphs in Chordal Graphs
We establish conditions for the existence, in a chordal graph, of subgraphs homeomorphic to Kn (n ≥ 3), Km,n (m,n ≥ 2), and wheels Wr (r ≥ 3). Using these results, we develop a simple linear time algorithm for testing planarity of chordal graphs. We also show how these results lead to simple polynomial time algorithms for the Fixed Subgraph Homeomorphism problem on chordal graphs for some speci...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009