We consider three probability measures on subsets of edges of a given finite graph G, namely those which govern, respectively, a uniform forest, a uniform spanning tree, and a uniform connected subgraph. A conjecture concerning the negative association of two edges is reviewed for a uniform forest, and a related conjecture is posed for a uniform connected subgraph. The former conjecture is veri...

In a two-capacitated spanning tree of a complete graph with a distinguished root vertex v, every component of the induced subgraph on V\{v} has at most two vertices. We give a complete, non-redundant characterization of the polytope defined by the convex hull of the incidence vectors of two-capacitated spanning trees. This polytope is the intersection of the spanning tree polytope on the given ...

In this paper we continue our investigations from [HM01] regarding spanning subgraphs which imply the existence of cycle double covers. We prove that if a cubic graph G has a spanning subgraph isomorphic to a subdivision of a bridgeless cubic graph on at most 10 vertices then G has a CDC. A notable result is thus that a cubic graph with a spanning Petersen minor has a CDC, a result also obtaine...

Suppose that T is a spanning tree of a graph G. T is called a locally connected spanning tree of G if for every vertex of T , the set of all its neighbors in T induces a connected subgraph of G. In this paper, given an intersection model of a circulararc graph, an O(n)-time algorithm is proposed that can determine whether the circular-arc graph contains a locally connected spanning tree or not,...

We present a new approximation algorithm for the minimum 2-edge-connected spanning subgraph problem. Its ratio is 43, which matches current best ratio. The of 65 on subcubic graphs, an improvement upon previous 54. novel extension primal-dual schema, consists two distinct phases. Both and analysis are much simpler than those approaches.

An undirected graph $G$ is known to both the prover $P$ and verifier $V$, but only knows a subgraph $H$ of $G$. Without revealing any information about $H$, wants convince $V$ that connected spanning $G$, i.e. contains all vertices In this paper, we propose an unconventional zero-knowledge proof protocol using physical deck cards, which enables physically show satisfies condition without it. We...

A straight-line grid drawing of a planar graph G is a drawing of G on an integer grid such that each vertex is drawn as a grid point and each edge is drawn as a straight-line segment without edge crossings. It is well known that a planar graph of n vertices admits a straight-line grid drawing on a grid of area O(n). A lower bound of Ω(n) on the area-requirement for straight-line grid drawings o...

Consider edge-colorings of the complete graph Kn. Let r(n, t) be the maximum number of colors in such a coloring that does not have t edge-disjoint rainbow spanning trees. Let s(n, t) be the maximum number of colors in such a coloring having no rainbow spanning subgraph with diameter at most t. We prove r(n, t) = (n−2 2 )

We prove a sufficient condition for a graph G to have a matching that interconnects all the components of a disconnected spanning subgraph ofG. The condition is derived from a recent extension of the Matroid intersection theorem due to Aharoni and Berger. We apply the result to the problem of the existence of a (spanning) 2-walk in sufficiently tough graphs.

Integration of concepts for the parallelization of image processing algorithms into parallel compiler technology. Abstract Given a Cartesian product G = G 1 : : : G m (m 2) of nontrivial connected graphs G i and the n{dimensional base B de Bruijn graph D = D B (n), it is investigated whether or not G is a spanning subgraph of D. Special attention is given to graphs G 1 : : : G m which are relev...