On a certain class of nonideal clutters
نویسندگان
چکیده
In this paper we define the class of near-ideal clutters following a similar concept due to Shepherd [Near perfect matrices, Math. Programming 64 (1994) 295–323] for near-perfect graphs. We prove that near-ideal clutters give a polyhedral characterization for minimally nonideal clutters as near-perfect graphs did for minimally imperfect graphs. We characterize near-ideal blockers of graphs as blockers of near-bipartite graphs. We find necessary conditions for a clutter to be near-ideal and sufficient conditions for the clutters satisfying that every minimal vertex cover is minimum. © 2006 Elsevier B.V. All rights reserved.
منابع مشابه
Imperfect and Nonideal Clutters: A Common Approach
We prove three theorems. First, Lovász’s theorem about minimal imperfect clutters, including also Padberg’s corollaries. Second, Lehman’s result on minimal nonideal clutters. Third, a common generalization of these two. The endeavor of working out a ‘common denominator’ for Lovász’s and Lehman’s theorems leads, besides the common generalization, to a better understanding and simple polyhedral p...
متن کاملAn extension of Lehman's theorem and ideal set functions
Lehman's theorem on the structure of minimally nonideal clutters is a fundamental result in polyhedral combinatorics. One approach to extending it has been to give a common generalization with the characterization of minimally imperfect clutters [15, 8]. We give a new generalization of this kind, which combines two types of covering inequalities and works well with the natural de nition of mino...
متن کاملResistant sets in the unit hypercube
Ideal matrices and clutters are prevalent in Combinatorial Optimization, ranging from balanced matrices, clutters of T -joins, to clutters of rooted arborescences. Most of the known examples of ideal clutters are combinatorial in nature. In this paper, rendered by the recently developed theory of cuboids, we provide a different class of ideal clutters, one that is geometric in nature. The advan...
متن کاملDeltas, delta minors and delta free clutters
For an integer n ≥ 3, the clutter ∆n := { {1, 2}, {1, 3}, . . . , {1, n}, {2, 3, . . . , n} } is called a delta of dimension n, whose members are the lines of a degenerate projective plane. In his seminal paper on non-ideal clutters, Alfred Lehman manifested the role of the deltas as a distinct class of minimally non-ideal clutters [DIMACS, 1990]. A clutter is delta free if it has no delta mino...
متن کاملIdeal clutters that do not pack
For a clutter C over ground set E, a pair of distinct edges e, f ∈ E are coexclusive if every minimal cover contains at most one of them. An identification of C is another clutter obtained after identifying coexclusive edges of C. If a clutter is non-packing, then so is any identification of it. Inspired by this observation, and impelled by the lack of a qualitative characterization for ideal m...
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:
- Discrete Applied Mathematics
دوره 154 شماره
صفحات -
تاریخ انتشار 2004