We adapt the classical 3-decomposition of any 2-connected graph to the case of simple graphs (no loops or multiple edges). By analogy with the block-cutpoint tree of a connected graph, we deduce from this decomposition a bicolored tree tc(g) associated with any 2-connected graph g, whose white vertices are the 3-components of g (3-connected components or polygons) and whose black vertices are b...

Let A = fC 1 ; C 2 ; : : : ; C n g be an arrangement of Jordan curves in the plane lying in general position, i.e., every curve properly intersects at least one other curve, no two curves touch each other and no three meet at a common intersection point. The Jordancurve arrangement graph of A has as its vertices the intersection points of the curves in A, and two vertices are connected by an ed...

Given a graph G, let fk be the number of forests of cardinality k in G. Then the sequence (fk) has been conjectured to be unimodal for any graph G. In this paper we confirm this conjecture for Kn and Kn,n by showing that the sequence for Kn is strictly increasing (when n ≥ 4) and the sequence for Kn,n is strictly increasing except for the very last term. As a corollary we also confirm the conje...

In this paper, we study path auction games in which multiple edges may be owned by the same agent. The edge costs and the set of edges owned by the same agent are privately known to the owner of the edges. In this setting, we show that, assuming that edges not on the winning path always get 0 payment, there is no individually rational, strategyproof mechanism in which only edge costs are report...

A graph is called supermagic if there is a labeling of edges where the edges are labeled with consecutive distinct positive integers such that the sum of the labels of all edges incident with any vertex is constant. A graph G is called degree-magic if there is a labeling of the edges by integers 1, 2, ..., |E(G)| such that the sum of the labels of the edges incident with any vertex v is equal t...

Let H be a graph having edges which has no loops and multiple edges. Complete results about the existence of colored designs CH |CK n with exactly colors, are established for 6 4 and for arbitrary when H is a matching or a star. In all cases when there is a design it can be chosen to be cyclic. Slightly less complete results are obtained when H is a path or a cycle. c © 2002 Elsevier Science B....

2. Main result. By an eulerian digraph we mean a digraph in which the in-degree is equal to the out-degree at each vertex. Let ED ME ( n, t) be the number of labelled loop-free eulerian digraphs with n vertices in which the multiplicity of each edge is at most t. Allowing loops would multiply ED ME (n, t) by exactly (t + 1) n, since loops do not affect the eulerian property. For the case where ...