Obstructions to a binary matroid being graphic
نویسندگان
چکیده
Bixby and Cunningham showed that a 3-connected binary matroid M is graphic if and only if every element belongs to at most two non-separating cocircuits. Likewise, Lemos showed that such a matroid M is graphic if and only if it has exactly r(M) + 1 nonseparating cocircuits. Hence the presence inM of either an element in at least three non-separating cocircuits, or of at least r(M) + 2 non-separating cocircuits, implies that M is non-graphic. We provide lower bounds on the size of the set of such elements, and on the number of non-separating cocircuits, in such non-graphic binary matroids. A computationally efficient method for finding such lower bounds for specific minor-closed classes of matroids is given. Applications of this method and other results on sets of obstructions to a binary matroid being graphic are given. © 2011 Elsevier Ltd. All rights reserved.
منابع مشابه
Outerplanar obstructions for matroid pathwidth
For each non-negative integer k, we provide all outerplanar obstructions for the class of graphs whose cycle matroid has pathwidth at most k. Our proof combines a decomposition lemma for proving lower bounds on matroid pathwidth and a relation between matroid pathwidth and linearwidth. Our results imply the existence of a linear algorithm that, given an outerplanar graph, outputs its matroid pa...
متن کاملRecognition Algorithms for Binary Signed-Graphic Matroids
In this paper we provide two recognition algorithms for the class of signed-graphic matroids along with necessary and sufficient conditions for a matroid to be signed-graphic. Specifically, we provide a polynomial-time algorithm which determines whether a given binary matroid is signed-graphic and an algorithm which determines whether a general matroid given by an independece oracle is binary s...
متن کاملCharacterizing graphic matroids by a system of linear equations
Given a rank-r binary matroid we construct a system of O(r) linear equations in O(r) variables that has a solution over GF(2) if and only if the matroid is graphic.
متن کاملA new characterization of graphic matroids
We give a necessary and sufficient condition for a binary matroid to be graphic. The condition is very natural, but, unlike other similar results, it gives a trivial algorithm for testing graphicness. © 2008 Elsevier Inc. All rights reserved.
متن کاملMatroid union - Graphic? Binary? Neither?
Graphic matroids form one of the most significant classes in matroid theory. When introducing matroids, Whitney concentrated on relations to graphs. The definition of some basic operations like deletion, contraction and direct sum were straightforward generalizations of the respective concepts in graph theory. Most matroid classes, for example those of binary, regular or graphic matroids, are c...
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:
- Eur. J. Comb.
دوره 32 شماره
صفحات -
تاریخ انتشار 2011