Edge disjoint caterpillar realizations

Wiring Edge-Disjoint Layouts

We consider the wiring or layer assignment problem for edge-disjoint layouts. The wiring problem is well understood for the case that the underlying layout graph is a square grid (see 7]). In this paper, we introduce a more general approach to this problem. For an edge-disjoint layout in the plane resp. in an arbitrary planar layout graph, we give equivalent conditions for the k-layer wirabilit...

4.1 Edge Disjoint Paths

Problem Statement: Given a directed graphG and a set of terminal pairs {(s1, t1), (s2, t2), · · · , (sk, tk)}, our goal is to connect as many pairs as possible using non edge intersecting paths. Edge disjoint paths problem is NP-Complete and is closely related to the multicommodity flow problem. In fact integer multicommodity flow is a generalization of this problem. We describe a greedy approx...

Edge Disjoint Spanning Trees ∗

Let Zm be the cyclic group of order m ≥ 3. A graph G is Zm-connected if G has an orientation D such that for any mapping b : V (G) 7→ Zm with ∑ v∈V (G) b(v) = 0, there exists a mapping f : E(G) 7→ Zm − {0} satisfying ∑ e∈E+ D (v) f(e) − ∑ e∈E− D (v) f(e) = b(v) in Zm for any v ∈ V (G); and a graph G is strongly Zm-connected if, for any mapping θ : V (G) → Zm with ∑ v∈V (G) θ(v) = |E(G)| in Zm, ...

Reconstructing edge-disjoint paths

Edge Disjoint Hamilton Cycles

In the late 70s, it was shown by Komlós and Szemerédi ([7]) that for p = lnn+ln lnn+c n , the limit probability for G(n, p) to contain a Hamilton cycle equals the limit probability for G(n, p) to have minimum degree at least 2. A few years later, Ajtai, Komlós and Szemerédi ([1]) have shown a hitting time version of this in the G(n,m) model. Say a graph G has property H if it contains bδ(G)/2c ...