Related papers: Coplanarity of rooted spanning-tree vectors
A \emph{$t$-treewidth-modulator} of a graph $G$ is a set $X \subseteq V(G)$ such that the treewidth of $G-X$ is at most some constant $t-1$. In this paper, we present a novel algorithm to compute a decomposition scheme for graphs $G$ that…
We study the large-deviation properties of minimum spanning trees for two ensembles of random graphs with $N$ nodes. First, we consider complete graphs. Second, we study Erd\H{o}s-R\'{e}nyi (ER) random graphs with edge probability $p=c/N$…
We present an analysis of the percolation transition for general node removal strategies valid for locally tree-like directed networks. On the basis of heuristic arguments we predict that, if the probability of removing node $i$ is $p_i$,…
In the present paper we consider the problem of constructing all the projective rooted spanning trees of a given graph. We propose an algorithm based on reducing this problem to the problem of constructing all the maximal independent sets…
Constrained counting is a fundamental problem in artificial intelligence. A promising new algebraic approach to constrained counting makes use of tensor networks, following a reduction from constrained counting to the problem of…
Vertex deletion and edge deletion problems play a central role in Parameterized Complexity. Examples include classical problems like Feedback Vertex Set, Odd Cycle Transversal, and Chordal Deletion. Interestingly, the study of edge…
The connection between the maximum spanning tree in a directed graph and the best dependency tree of a sentence has been exploited by the NLP community. However, for many dependency parsing schemes, an important detail of this approach is…
Packing graphs is a combinatorial problem where several given graphs are being mapped into a common host graph such that every edge is used at most once. In the planar tree packing problem we are given two trees T1 and T2 on n vertices and…
We propose a novel linearization of a constituent tree, together with a new locally normalized model. For each split point in a sentence, our model computes the normalizer on all spans ending with that split point, and then predicts a tree…
It is folklore that tree-width is monotone under taking subgraphs (i.e. injective graph homomorphisms) and contractions (certain kinds of surjective graph homomorphisms). However, although tree-width is obviously not monotone under any…
We prove a Matrix-Tree Theorem enumerating the spanning trees of a cell complex in terms of the eigenvalues of its cellular Laplacian operators, generalizing a previous result for simplicial complexes. As an application, we obtain explicit…
In the 1970's, Balas introduced the concept of disjunctive programming, which is optimization over unions of polyhedra. One main result of his theory is that, given linear descriptions for each of the polyhedra to be taken in the union, one…
We study the problem of decomposing (clustering) a tree with respect to costs attributed to pairs of nodes, so as to minimize the sum of costs for those pairs of nodes that are in the same component (cluster). For the general case and for…
Given a spanning tree $T$ of a planar graph $G$, the co-tree of $T$ is the spanning tree of the dual graph $G^*$ with edge set $(E(G)-E(T))^*$. Gr\"unbaum conjectured in 1970 that every planar 3-connected graph $G$ contains a spanning tree…
We consider the class of graphs for which the edge connectivity is equal to the maximum number of edge-disjoint spanning trees, and the natural generalization to matroids, where the cogirth is equal to the number of disjoint bases. We…
The tree-loop duality relation is used as a starting point to derive the constraints of causality and unitarity. Specifically, the Bogoliubov causality condition is ab initio derived at the individual graph level. It leads to a…
Previous AutoML pruning works utilized individual layer features to automatically prune filters. We analyze the correlation for two layers from the different blocks which have a short-cut structure. It shows that, in one block, the deeper…
Vertex deletion to hereditary graph class is well-studied in parameterized complexity. Vertex deletion to the scattered graph classes has gained attention in recent years. In this paper, we consider (Proper-Interval, Tree)-Vertex Deletion,…
We obtain polynomial-time approximation-preserving reductions (up to a factor of 1 + \epsilon) from the prize-collecting Steiner tree and prize-collecting Steiner forest problems in planar graphs to the corresponding problems in graphs of…
Consider a tree $T=(V,E)$ with root $\circ$ and edge length function $\ell:E\to\mathbb{R}_+$. The phylogenetic covariance matrix of $T$ is the matrix $C$ with rows and columns indexed by $L$, the leaf set of $T$, with entries…