P.D. Seymour proved that the cut criterion is necessary and suucient for the solvability of the edge-disjoint paths problem when the union of the supply graph and the demand graph is planar and Eulerian. When only planarity is required, M. Middendorf and F. Pfeiier proved the problem to be NP-complete. For this case E. Korach and M. Penn proved that the cut criterion is suucient for the existen...

An edge cut of a connected graph is 5-restricted if its removal leaves every component having order at least five. Graphs that contain 5-restricted edge cuts are characterized in this paper. As a result, it is shown that a connected graph G of order at least 13 contains 5-restricted edge cuts if and only if G \ v contains a component of order at least five for every vertex v of graph G.

We develop a theory of factorisation of snarks — cubic graphs with edge-chromatic number 4 — based on the classical concept of the dot product. Our main concern are irreducible snarks, those where the removal of every nontrivial edge-cut yields a 3-edge-colourable graph. We show that if an irreducible snark can be expressed as a dot product of two smaller snarks, then both of them are irreducib...

We study survivable network design problems with edge-connectivity requirements under a two-stage stochastic model with recourse and finitely many scenarios. For the formulation in the natural space of edge variables we show that facet defining inequalities of the underlying polytope can be derived from the deterministic counterparts. Moreover, by using graph orientation properties we introduce...

Graph computation system performance is generally affected by the quality of graph partition. The balance factor and small edge cut ratio is used to measure the quality of graph partition. A balance graph partition with small edge cut ratio is generally preferred since it cut down the expensive network communication cost. Even so, according to the study of the Giraph, the execution over well pa...

In this paper, we find the relationship between mincut circuit partitioning and the initial (V, E) pairs distributed condition I entropy on the V-E plain. If a circuit has higher initial potential / entropy, under a nearly max-cut reservation, we have higher probability to aim the mincut. The proposed new method is called Interleaved Cutting Edge-Node Interleaved Sort for Leaching and Envelop (...

In the CUT PACKING problem, given an undirected connected graph G, it is required to nd the maximum number of pairwise edge disjoint cuts in G. It is an open question if CUT PACKING is NP-hard on general graphs. In this paper we prove that the problem is polynomially solvable on Seymour graphs which include both all bipar-tite and all series-parallel graphs. We also consider the weighted versio...

We investigate the supereulerian graph problems within planar graphs, and we prove that if a 2-edge-connected planar graph G is at most three edges short of having two edge-disjoint spanning trees, then G is supereulerian except a few classes of graphs. This is applied to show the existence of spanning Eulerian subgraphs in planar graphs with small edge cut conditions. We also determine several...

Some results on matchings in a hypergraph cut vertex, cut edge of hypergraph have been obtained analogous to the results in a simple graph. In this paper we have obtained some interesting properties of a hypergraph. The notations and terminology that are used in this paper are the same as in [1].

The super (resp., edge-) connectivity of a connected graph is the minimum cardinality of a vertex-cut (resp., an edge-cut) whose removal does not isolate a vertex. In this paper, we consider the two parameters for a special class of graphs G(G0, G1; M), proposed by Chen et al [Applied Math. and Computation, 140 (2003), 245-254], obtained from two k-regular k-connected graphs G0 and G1 with the ...