相关论文: A new strategy for finding spanning trees without …
In the laminar-constrained spanning tree problem, the goal is to find a minimum-cost spanning tree which respects upper bounds on the number of times each cut in a given laminar family is crossed. This generalizes the well-studied…
Given a set of points in the Euclidean plane, the Euclidean \textit{$\delta$-minimum spanning tree} ($\delta$-MST) problem is the problem of finding a spanning tree with maximum degree no more than $\delta$ for the set of points such the…
The problem of spanning trees is closely related to various interesting problems in the area of statistical physics, but determining the number of spanning trees in general networks is computationally intractable. In this paper, we perform…
We consider lower bounds on the number of spanning trees of connected graphs with degree bounded by $d$. The question is of interest because such bounds may improve the analysis of the improvement produced by memorisation in the runtime of…
We consider the problem of computing a Steiner tree of minimum cost under a hop constraint which requires the depth of the tree to be at most $k$. Our main result is an exact algorithm for metrics induced by graphs with bounded treewidth…
We investigate the computation of minimum-cost spanning trees satisfying prescribed vertex degree constraints: Given a graph $G$ and a constraint function $D$, we ask for a (minimum-cost) spanning tree $T$ such that for each vertex $v$, $T$…
We consider the classical problems (Edge) Steiner Tree and Vertex Steiner Tree after restricting the input to some class of graphs characterized by a small set of forbidden induced subgraphs. We show a dichotomy for the former problem…
We consider the k-outconnected directed Steiner tree problem (k-DST). Given a directed edge-weighted graph $G=(V,E,w)$, where $V=\{r\}\cup S \cup T$, and an integer $k$, the goal is to find a minimum cost subgraph of $G$ in which there are…
Processing graphs with temporal information (the temporal graphs) has become increasingly important in the real world. In this paper, we study efficient solutions to temporal graph applications using new algorithms for Incremental Minimum…
Bounded-angle (minimum) spanning trees were first introduced in the context of wireless networks with directional antennas. They are reminiscent of bounded-degree spanning trees, which have received significant attention. Let $P =…
We present a new characterization of $k$-trees based on their reduced clique graphs and $(k+1)$-line graphs, which are block graphs. We explore structural properties of these two classes, showing that the number of clique-trees of a…
With the rapid development of mobile computing and Web services, a huge amount of data with spatial and temporal information have been collected everyday by smart mobile terminals, in which an object is described by its spatial information…
Let $G$ be a graph with a spanning subgraph $F$, let $m$ be a positive integer, and let $f$ be a positive integer-valued function on $V(G)$. In this paper, we show that if for all $S\subseteq V(G)$, $$\Omega_m(G\setminus S)\le \sum_{v\in…
We study the problem of maximizing the number of full degree vertices in a spanning tree $T$ of a graph $G$; that is, the number of vertices whose degree in $T$ equals its degree in $G$. In cubic graphs, this problem is equivalent to…
Working with tree graphs is always easier than with loopy ones and spanning trees are the closest tree-like structures to a given graph. We find a correspondence between the solutions of random K-satisfiability problem and those of spanning…
A simple graph $G$ is an {\it 2-tree} if $G=K_3$, or $G$ has a vertex $v$ of degree 2, whose neighbors are adjacent, and $G-v$ is an 2-tree. Clearly, if $G$ is an 2-tree on $n$ vertices, then $|E(G)|=2n-3$. A non-increasing sequence…
Streaming decision trees are natural candidates for open-world continual learning, as they perform local updates, enjoy bounded memory, and static decision boundaries. Despite these, they still fail in online class-incremental learning due…
The middle-levels graph $M_k$ ($0<k\in\mathbb{Z}$) has a dihedral quotient pseudograph $R_k$ whose vertices are the $k$-edge ordered trees $T$, each $T$ encoded as a $(2k+1)$-string $F(T)$ formed via $\rightarrow$DFS by: {\bf(i)}…
In this article, we extend Moon's classic formula for counting spanning trees in complete graphs containing a fixed spanning forest to complete bipartite graphs. Let $(X,Y)$ be the bipartition of the complete bipartite graph $K_{m,n}$ with…
We study a natural problem in graph sparsification, the Spanning Tree Congestion (\STC) problem. Informally, the \STC problem seeks a spanning tree with no tree-edge \emph{routing} too many of the original edges. The root of this problem…