Lehman / s Switching Tutte and Game and a Theorem of Nash - Williams l Jack Edmonds

نویسنده

  • Jack Edmonds
چکیده

The results c ited in the title are unifi ed by th e following theore m: For a ny matroid M a nd any subse ts Nand K of e le me nts in M , there e xi s t as many as k disjoint subsets of N which span K a nd which spa n each ot he r if and only if the re is no contraction matroid M X A where NnA partitions int o as few as k se ts such th at eac h is independen t in M X A and suc h that at least one of the m does not s pan KnA in M x A.

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

Ore, Berge–Tutte, and Gallai–Edmonds

We present a short proof of the Berge–Tutte Formula and the Gallai–Edmonds Structure Theorem based on Ore’s Defect Formula and Anderson’s proof of Tutte’s 1-Factor Theorem from Hall’s Theorem. The fundamental theorems on matchings in graphs have been proved in many ways, and generally they all imply each other. The most well-known is Hall’s Theorem [7] characterizing when a bipartite graph has ...

متن کامل

Reinforcing a Matroid to Have k Disjoint Bases

Let ( ) M  denote the maximum number of disjoint bases in a matroid M . For a connected graph G , let ( ) = ( ( )) G M G   , where ( ) M G is the cycle matroid of G . The well-known spanning tree packing theorem of Nash-Williams and Tutte characterizes graphs G with ( ) G k   . Edmonds generalizes this theorem to matroids. In [1] and [2], for a matroid M with ( ) M k   , elements ( ) e E...

متن کامل

The Hypergraphic Tutte/Nash-Williams Theorem via Integer Decomposition, Total Dual Laminarity, and Power Matroids

We reprove the hypergraphic generalization of the Tutte/Nash-Williams theorem, which gives sufficient conditions for a hypergraph to contain k disjoint connected hypergraphs. First we observe the theorem is equivalent to the natural LP relaxation having the integer decomposition property. Then we give a new proof of this property using LP uncrossing methods. We discover that “total dual laminar...

متن کامل

Sparse Hypergraphs and Pebble Game Algorithms

A hypergraph G = (V, E) is (k, `)-sparse if no subset V ′ ⊂ V spans more than k|V ′|−` hyperedges. We characterize (k, `)-sparse hypergraphs in terms of graph theoretic, matroidal and algorithmic properties. We extend several well-known theorems of Haas, Lovász, Nash-Williams, Tutte, and White and Whiteley, linking arboricity of graphs to certain counts on the number of edges. We also address t...

متن کامل

Arboricity and tree-packing in locally finite graphs

Nash-Williams’ arboricity theorem states that a finite graph is the edge-disjoint union of at most k forests if no set of ` vertices induces more than k(`− 1) edges. We prove a natural topological extension of this for locally finite infinite graphs, in which the partitioning forests are acyclic in the stronger sense that their Freudenthal compactification—the space obtained by adding their end...

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:

دوره   شماره 

صفحات  -

تاریخ انتشار 2010