Nowhere zero flow and circuit covering in regular matroids
نویسندگان
چکیده
منابع مشابه
Nowhere zero 4-flow in regular matroids
Jensen and Toft [10] conjectured that every 2-edge-connected graph without a K5minor has a nowhere zero 4-flow. Walton and Welsh [24] proved that if a coloopless regular matroid M does not have a minor in {M(K3,3),M(K5)}, then M admits a nowhere zero 4-flow. In this note, we prove that if a coloopless regular matroid M does not have a minor in {M(K5),M(K5)}, then M admits a nowhere zero 4-flow....
متن کاملNowhere-zero Flows in Regular Matroids and Hadwiger’s Conjecture
We present a tool that shows, that the existence of a k-nowhere-zero-flow is compatible with 1-,2and 3-sums in regular matroids. As application we present a conjecture for regular matroids that is equivalent to Hadwiger’s conjecture for graphs and Tuttes’s 4and 5-flow conjectures.
متن کاملNowhere-zero flow polynomials
In this article we introduce the flow polynomial of a digraph and use it to study nowherezero flows from a commutative algebraic perspective. Using Hilbert’s Nullstellensatz, we establish a relation between nowhere-zero flows and dual flows. For planar graphs this gives a relation between nowhere-zero flows and flows of their planar duals. It also yields an appealing proof that every bridgeless...
متن کاملNowhere-zero flows on signed regular graphs
We study the flow spectrum S(G) and the integer flow spectrum S(G) of odd regular graphs. We show that there are signed graphs where the difference between the integer flow number and the flow number is greater than or equal to 1, disproving a conjecture of Raspaud and Zhu [7]. Let G be a (2t + 1)-regular graph. We show that if r ∈ S(G), then r = 2 + 1t or r ≥ 2 + 2 2t−1 . This result generaliz...
متن کاملCovering Vectors by Spaces: Regular Matroids
We consider 5the problem of covering a set of vectors of a given finite dimensional linear space (vector space) by a subspace generated by a set of vectors of minimum size. Specifically, we study the Space Cover problem, where we are given a matrix M and a subset of its columns T ; the task is to find a minimum set F of columns of M disjoint with T such that that the linear span of F contains 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
ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1985
ISSN: 0095-8956
DOI: 10.1016/0095-8956(85)90059-0