This paper addresses a problem posed by Oxley (Matroid Theory, Cambridge University Press, Cambridge, 1992) for matroids.We shall show that ifG is a 2-connected graph which is not a multiple edge, and which has no K5-minor, then G has two edge-disjoint non-trivial bonds B for which G/B is 2-connected. © 2004 Elsevier Inc. All rights reserved. MSC: 05C38; 05C40; 05C70

In this note, we consider the problem of existence of an edgedecomposition of a multigraph into isomorphic copies of 2-edge paths K1,2. We find necessary and sufficient conditions for such a decomposition of a multigraph H to exist when (i) either H does not have incident multiple edges or (ii) multiplicities of the edges in H are not greater than two. In particular, we answer a problem stated ...

the edges of an image define the image boundary. when the image is noisy, it does not become easy to identify the edges. therefore, a method requests to be developed that can identify edges clearly in a noisy image. many methods have been proposed earlier using filters, transforms and wavelets with ant colony optimization (aco) that detect edges. we here used aco for edge detection of noisy ima...

We study the problem of fixturing a chain of hinged objects in a given placement with frictionless point contacts. We define the notions of immobility and robust immobility, which are comparable to second and first order immobility for a single object [8, 7, 11, 12] robust immobility differs from immobility in that it additionally requires insensitivity to small perturbations of contacts. We sh...

We study path auction games in which multiple edges may be owned by the same agent in this paper. The edge costs and the set of edges owned by the same agent are privately known to the owner of the edge. We show that in this setting, given the assumption the losing agent always has 0 payoff, there is no individual rational strategyproof mechanism in which only edge costs are reported. If the ag...

We prove a Riemann-Roch theorem for real divisors on edgeweighted graphs over the reals, extending the result of Baker and Norine for integral divisors on graphs with multiple edges.

We prove a Riemann-Roch theorem for real divisors on edge-weighted graphs over the reals, extending the result of Baker and Norine for integral divisors on graphs with multiple edges.

It is easy to characterize graphs with no Kk-minors for any integer k ≤ 4, as follows. For k = 1, 2, the problem must be trivial, and for k = 3, 4, those graphs are forests and series-parallel graphs (i.e., graphs obtained from K3 by a sequence of replacing a vertex of degree 2 with a pair of parallel edges, or its inverse operation.) Moreover, Wagner formulated a fundamental characterization o...

Let G be a simple (i.e., no loops and no multiple edges) graph. We investigate the question of how to modify G combinatorially to obtain a sequentially CohenMacaulay graph. We focus on modifications given by adding configurations of whiskers to G, where to add a whisker one adds a new vertex and an edge connecting this vertex to an existing vertex in G. We give various sufficient conditions and...

Motivated by the necessities of the invariant theory of binary forms J. J. Sylvester constructed in 1878 for each graph with possible multiple edges but without loops its symmetrized graph monomial which is a polynomial in the vertex labels of the original graph. We pose the question for which graphs this polynomial is a non-negative resp. a sum of squares. This problem is motivated by a recent...