We study uniform spanning forest measures on infinite graphs, which are weak limits of uniform spanning tree measures from finite subgraphs. These limits can be taken with free (FSF) or wired (WSF) boundary conditions. Pemantle (1991) proved that the free and wired spanning forests coincide in Z d and that they give a single tree iff d 6 4. In the present work, we extend Pemantle’s alternative ...

We study uniform spanning forest measures on innnite graphs, which are weak limits of uniform spanning tree measures from nite subgraphs. These limits can be taken with free (FSF) or wired (WSF) boundary conditions. Pemantle (1991) proved that the free and wired spanning forests coincide in Z d and that they give a single tree ii d 6 4. In the present work, we extend Pemantle's alternative to g...

Let G be a connected claw-free graph. A conjecture of Matsuda, Ozeki, and Yamashita [9] posits the existence of either a spanning tree with few branch vertices or a large independent set of small degree sum. The possible appearances of this minimal spanning tree may be ruled out piecemeal. This paper treats one particular class, which may be the easiest to rule out but also fits, to our knowled...

For a planar point set we consider the graph of crossing-free straight-line spanning trees where two spanning trees are adjacent in the graph if their union is crossing-free. An upper bound on the diameter of this graph implies an upper bound on the diameter of the flip graph of pseudo-triangulations of the underlying point set. We prove a lower bound of Ω ( log(n)/ log(log(n)) ) for the diamet...

A k-tree is a tree with maximum degree at most k, and a k-walk is a closed walk with each vertex repeated at most k times. A k-walk can be obtained from a k-tree by visiting each edge of the k-tree twice. Jackson and Wormald conjectured in 1990 that for k ≥ 2, every 1 k−1 -tough connected graph contains a spanning k-walk. This conjecture is open even for planar graphs. We confirm this conjectur...

A b s t r a c t. We show in set-theory ZF that the axiom of choice is equivalent to the statement every bipartite connected graph has a spanning sub-graph omitting some complete finite bipartite graph K n,n , and in particular it is equivalent to the fact that every connected graph has a spanning cycle-free graph (possibly non connected). We consider simple undirected loop-free graphs. A forest...

The Tutte polynomial of a graph is a 2-variable polynomial which is quite important in both combinatorics and statistical physics. It contains various numerical invariants and polynomial invariants ,such as the number of spanning trees,the number of spanning forests , the number of acyclic orientations , the reliability polynomial,chromatic polynomial and flow polynomial . In this paper,we stud...

In this paper we propose a deadlock free routing in irregular networks using pre x routing Pre x routing is a special type of routing with a compact routing table associated with each node processor Basically each outgoing channel of a node is assigned a special label and an outgoing channel is selected if its label is a pre x of the label of the destination node Node and channel labeling in an...

We study the maximal number of triangulations that a planar set of n points can have, and show that it is at most 30n. This new bound is achieved by a careful optimization of the charging scheme of Sharir and Welzl (2006), which has led to the previous best upper bound of 43n for the problem. Moreover, this new bound is useful for bounding the number of other types of planar (i.e., crossing-fre...