Antisymmetric flows and edge-connectivity

Antisymmetric flows in matroids

We present a seemingly new definition of flows and flow numbers for oriented matroids and prove that the flow number ΦL and the antisymmetric flow number ΦLas of an oriented matroid are bounded with its rank. In particular we show that if O is an oriented matroid of rank r then ΦL(O) ≤ r + 2 and ΦLas(O) ≤ 3b 9 2 rc+1. Furthermore, we introduce the notion of a semiflow and show that each oriente...

A note on antisymmetric flows in graphs

We prove that any orientation of a graph without bridges and directed 2-edge-cuts admits a Z2 ×Z3-antisymmetric flow, which improves the bounds obtained by DeVos, Johnson and Seymour, and DeVos, Nešetřil and Raspaud.

Edge-connectivity and super edge-connectivity of P2-path graphs

For a graph G, the P2-path graph, P2(G), has for vertices the set of all paths of length 2 in G. Two vertices are connected when their union is a path or a cycle of length 3. We present lower bounds on the edge-connectivity, (P2(G)) of a connected graph G and give conditions for maximum connectivity. A maximally edge-connected graph is superif each minimum edge cut is trivial, and it is optimum...

Antisymmetric flows and strong oriented coloring of planar graphs

Edge-connectivity and edge-disjoint spanning trees

where the minimum is taken over all subsets X of E(G) such that ω(G − X) − c > 0. In this paper, we establish a relationship 7 between λc(G) and τc−1(G), which gives a characterization of the edge-connectivity of a graph G in terms of the spanning tree 8 packing number of subgraphs of G. The digraph analogue is also obtained. The main results are applied to show that if a graph G is 9 s-hamilto...