Local edge-connectivity in regular bipartite graphs

Edge-connectivity augmentations of bipartite graphs

Given a bipartite graph, the bipartite global edge-connectivity aug-mentation problem consists of finding a minimum cardinality edge setwhose addition results in a bipartite k-edge-connected graph. A min-imax theorem and some applications will be presented. This part ofthe talk is based on [1].I will also mention some preliminary results from [2] concerning thelocal ...

Matching and edge-connectivity in regular graphs

Henning and Yeo proved a lower bound for the minimum size of a maximum matching in a connected k-regular graphs with n vertices; it is sharp infinitely often. In an earlier paper, we characterized when equality holds. In this paper, we prove a lower bound for the minimum size of a maximum matching in an l-edge-connected k-regular graph with n vertices, for l ≥ 2 and k ≥ 4. Again it is sharp for...

Restricted Edge Connectivity of Regular Graphs

An edge cut that separates the connected graph into components with order at least two is restricted edge cut. The cardinality of minimum restricted edge cut is restricted edge connectivity. Denote byλ′ ( G) the restricted edge connectivity , then λ′( G) ≤ξ( G) where ξ( G) is the minimum edge degree. G is called maximal restricted edge connected if the equality in the previous inequality holds....

Eigenvalues and edge-connectivity of regular graphs

In this paper, we show that if the second largest eigenvalue of a d-regular graph is less than d − 2(k−1) d+1 , then the graph is k-edge-connected. When k is 2 or 3, we prove stronger results. Let ρ(d) denote the largest root of x3 − (d− 3)x2 − (3d− 2)x− 2 = 0. We show that if the second largest eigenvalue of a d-regular graph G is less than ρ(d), then G is 2-edge-connected and we prove that if...

Finding 1-Factors in Bipartite Regular Graphs and Edge-Coloring Bipartite Graphs