Graphical representations of clutters

نویسندگان

  • Michael Dinitz
  • Jonah M. Gold
  • Thomas C. Sharkey
  • Lorenzo Traldi
چکیده

We discuss the use of K-terminal networks to represent arbitrary clutters. A given clutter has many di¤erent representations, and there does not seem to be any set of simple transformations that can be used to transform one representation of a clutter into any other. We observe that for t 2 the class of clutters that can be represented using no more than t terminals is closed under minors, and has in…nitely many forbidden minors.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Resistant 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 کامل

Deltas, 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 کامل

On 2-partitionable clutters and the MFMC property

We introduce 2-partitionable clutters as the simplest case of the class of kpartitionable clutters and study some of their combinatorial properties. In particular, we study properties of the rank of the incidence matrix of these clutters and properties of their minors. A well known conjecture of Conforti and Cornuéjols [1, 2] states: That all the clutters with the packing property have the max-...

متن کامل

Ideal 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 کامل

Bounding the Projective Dimension of a Squarefree Monomial Ideal via Domination in Clutters

We introduce the concept of edgewise domination in clutters, and use it to provide an upper bound for the projective dimension of any squarefree monomial ideal. We then compare this bound to a bound given by Faltings. Finally, we study a family of clutters associated to graphs and compute domination parameters for certain classes of these clutters.

متن کامل

ذخیره 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 نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Ars Comb.

دوره 94  شماره 

صفحات  -

تاریخ انتشار 2010