The problem of constructing independent spanning trees (ISTs) dates back to as early the late 1980s. Given a network G certain topology, question is whether we can, well how to, construct set ISTs in . have proven be great importance many tasks. past decade has seen particularly remarkable increase literature on ISTs, manifesting significant growth interest. can classified into edge-independent...

We show that the local limit of uniform spanning tree on any finite, simple, connected, regular graph sequence with degree tending to $$\infty $$ is Poisson(1) branching process conditioned survive forever. An extension “almost” graphs and a quenched version are also given.

We study the multicolour discrepancy of spanning trees and Hamilton cycles in graphs. As our main result, we show that under very mild conditions, r-colour spanning-tree a graph G is equal, up to constant, minimum s such can be separated into r equal parts by deleting vertices. This result arguably resolves question estimating essentially all graphs interest. In particular, it allows us immedia...

Let $G=(V, E)$ be an undirected graph. The spanning trees polytope $P(G)$ is the convex hull of characteristic vectors all $G$. In this paper, we describe facets as a consequence bases $P(M)$ matroid $M$, i.e., $M$.

Feature selection is a fundamental process to avoid overfitting and reduce the size of databases without significant loss information that applies hierarchical clustering. Dendrograms are graphical representations clustering algorithms for single linkage can be interpreted as minimum spanning trees in complete network defined by database. In this work, we introduce problem determines jointly se...

Let LTQn denote the n-dimensional locally twisted cube. Hsieh and Tu (2009) [13] presented an algorithm to construct n edge-disjoint spanning trees rooted at vertex 0 in LTQn. Later on, Lin et al. (2010) [23] proved that Hsieh and Tu’s spanning trees are indeed independent spanning trees (ISTs for short), i.e., all spanning trees are rooted at the same vertex r and for any other vertex v(6= r),...