Chain Decompositions of 4-Connected Graphs

Chain Decompositions of 4-Connected Graphs

In this paper we give a decomposition of a 4-connected graph G into nonseparating chains, which is similar to an ear decomposition of a 2-connected graph. We also give an O(|V (G)||E(G)|) algorithm that constructs such a decomposition. In applications, the asymptotic performance can often be improved to O(|V (G)|). This decomposition will be used to find four independent spanning trees in a 4co...

On 4-connected graphs without even cycle decompositions

4-Cycle Decompositions of Graphs

In this paper we consider the problem of finding the smallest number  such that any graph G of order n admits a decomposition into edge disjoint copies of C4 and single edges with at most  elements. We solve this problem for n sufficiently large.

Generating 4-connected graphs

5 Let C = {C n : n ≥ 5} and let L = {G : G is the line graph of an internally 4-connected cubic graph}. 6 A classical result of Martinov states that every 4-connected graph G can be constructed from graphs in 7 C ∪L by repeatedly splitting vertices. In this paper we prove that, in fact, G can be constructed from C 5 8 or C 6 in the same way, unless G belongs to C ∪L. Moreover, if G is nonplanar...

Decompositions of highly connected graphs into paths of length five

We prove that a 171-edge-connected graph has an edgedecomposition into paths of length 3 if and only its size is divisible by 3. It is a long-standing problem whether 2-edge-connectedness is sufficient for planar triangle-free graphs, andwhether 3-edge-connectedness suffices for graphs in general. © 2008 Wiley Periodicals, Inc. J Graph Theory 58: 286–292, 2008 Keyword: path-decompositions