Mixed Search Number and Linear-Width of Interval and Split Graphs
نویسندگان
چکیده
We show that the mixed search number and the linear-width of interval graphs and of split graphs can be computed in linear time and in polynomial time, respectively.
منابع مشابه
Algorithms and Obstructions for Linear-width and Related Search Parameters 1
The linear-width of a graph G is deened to be the smallest integer k such that the edges of G can be arranged in a linear ordering (e 1 ; : : :; e r) in such a way that for every i = 1; : : :; r ? 1, there are at most k vertices incident to edges that belong both to fe 1 ; : : :; e i g and to fe i+1 ; : : :; e r g. In this paper, we give a set of 57 graphs and prove that it is the set of the mi...
متن کاملAlgorithms and obstructions for linear-width and related search parameters
The linear-width of a graph G is de ned to be the smallest integer k such that the edges of G can be arranged in a linear ordering (e1; : : : ; er) in such a way that for every i = 1; : : : ; r 1, there are at most k vertices incident to edges that belong both to fe1; : : : ; eig and to fei+1; : : : ; erg. In this paper, we give a set of 57 graphs and prove that it is the set of the minimal for...
متن کاملExploiting Restricted Linear Structure to Cope with the Hardness of Clique-Width
Clique-width is an important graph parameter whose computation is NP-hard. In fact we do not know of any other algorithm than brute force for the exact computation of clique-width on any non-trivial graph class. Results so far indicate that proper interval graphs constitute the first interesting graph class on which we might have hope to compute clique-width, or at least its linear variant line...
متن کاملFast-Mixed Searching on Graphs
We introduce the fast-mixed search model, which is a combination of the fast search model and the mixed search model. We establish relations between the fast-mixed search problem and other graph search problems. We also establish relations between the fast-mixed search problem and the inducedpath cover problem. We present linear-time algorithms for computing the fast-mixed search number and opt...
متن کاملUpper Bounds on Boolean-Width with Applications to Exact Algorithms
Boolean-width is similar to clique-width, rank-width and NLC-width in that all these graph parameters are constantly bounded on the same classes of graphs. In many classes where these parameters are not constantly bounded, boolean-width is distinguished by its much lower value, such as in permutation graphs and interval graphs where boolean-width was shown to be O(logn) [1]. Together with FPT a...
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 2007