Graph Connectivity and Network Coding LEUNG, Kai Man Master of Philosophy Department of Computer Science and Engineering The Chinese University of Hong Kong 2011 In this thesis we present a new algebraic formulation to compute edge connectivities in a directed graph, using the ideas developed in network coding. This reduces the problem of computing edge connectivities to solving systems of line...

The universal cyclic edge-connectivity of a graph G is the least k such that there exists set edges whose removal disconnects into components where every component contains cycle. We show for graphs minimum degree at 3 and girth g 4, bounded above by \((\Delta -2)g\) \(\Delta \) maximum degree. then prove if second eigenvalue adjacency matrix d-regular \(g\ge 4\) sufficiently small, \((d-2)g\),...

We present a specialised constraint for enforcing graph connectivity. It is assumed that we have a square symmetrical array A of 0/1 constrained integer variables representing potential undirected edges in a simple graph, such that variable A[u, v] corresponds to the undirected edge (u, v). A search process is then at liberty to select and reject edges. The connectivity constraint ensures that ...

We prove a decomposition result for locally finite graphs which can be used to extend results on edge-connectivity from finite to infinite graphs. It implies that every 4k-edge-connected graph G contains an immersion of some finite 2k-edge-connected Eulerian graph containing any prescribed vertex set (while planar graphs show that G need not contain a subdivision of a simple finite graph of lar...