Related papers: Bridge graphs and Deodhar parametrizations for pos…
A threshold graph G on n vertices is defined by binary sequence of length n. In this paper we present an explicit formula for computing the characteristic polynomial of a threshold graph from its binary sequence. Applications include…
In the Directed Steiner Network problem, the input is a directed graph G, a subset T of k vertices of G called the terminals, and a demand graph D on T. The task is to find a subgraph H of G with the minimum number of edges such that for…
In this paper, we introduce a family of tetravalent graphs called propeller graphs, denoted by $Pr_{n}(b,c,d)$. We then produce three infinite subfamilies and one finite subfamily of arc-transitive propeller graphs, and show that all such…
Connections between structural graph theory and finite model theory recently gained a lot of attention. In this setting, many interesting questions remain on the properties of dependent (NIP) hereditary classes of graphs, in particular…
We introduce the graph theoretical parameter of edge treewidth. This parameter occurs in a natural way as the tree-like analogue of cutwidth or, alternatively, as an edge-analogue of treewidth. We study the combinatorial properties of…
This paper introduces Dirichlet matroids, a generalization of graphic matroids arising from electrical networks. We present four main theorems. First, we exhibit a matroid quotient involving geometric duals of networks embedded in surfaces…
AThe paper gives a few arguments in favour of the use of chain graphs for description of probabilistic conditional independence structures. Every Bayesian network model can be equivalently introduced by means of a factorization formula with…
We introduce a binary matroid M(IAS(G)) associated with a looped simple graph G. M(IAS(G)) classifies G up to local equivalence, and determines the delta-matroid and isotropic system associated with G. Moreover, a parametrized form of its…
Grothendieck's theory of dessins provides a bridge between algebraic numbers and combinatorics. This paper adds a new concept, called 'bias', to the bridge. This produces: (i) from a biased plane tree the construction of a sequence of…
We define two families of determinantal random spanning subgraphs of a finite connected graph, one supported by acyclic spanning subgraphs (spanning forests) with fixed number of connected components, the other by connected spanning…
Graph structure expression plays a vital role in distinguishing various graphs. In this work, we propose a Structure-Sensitive Graph Dictionary Embedding (SS-GDE) framework to transform input graphs into the embedding space of a graph…
The generalized composition graph is used by Cardoso and some researchers for factorization of the adjacency spectrum and Laplacian of a simple graph. Because the generalized composition graph is an example of a set-theoretic linear operad,…
Traditionally, graph algorithms get a single graph as input, and then they should decide if this graph satisfies a certain property $\Phi$. What happens if this question is modified in a way that we get a possibly infinite family of graphs…
The definition of $1$-planar graphs naturally extends graph planarity, namely a graph is $1$-planar if it can be drawn in the plane with at most one crossing per edge. Unfortunately, while testing graph planarity is solvable in linear time,…
We introduce a class of parameterised counting problems on graphs, p-#Induced Subgraph With Property(\Phi), which generalises a number of problems which have previously been studied. This paper focusses on the case in which \Phi defines a…
Consider a collection of points in the plane and the sets of slopes or directions of the lines between pairs of points. It is known that the algebraic matroid on the set of direction constraints between the points is equivalent to the…
While deep convolutional architectures have achieved remarkable results in a gamut of supervised applications dealing with images and speech, recent works show that deep untrained non-convolutional architectures can also outperform…
Tree-width and path-width are well-known graph parameters. Many NP-hard graph problems allow polynomial-time solutions, when restricted to graphs of bounded tree-width or bounded path-width. In this work, we study the behavior of tree-width…
A mixed graph contains (undirected) edges as well as (directed) arcs, thus generalizing undirected and directed graphs. A proper coloring $c$ of a mixed graph $G$ assigns a positive integer to each vertex such that $c(u)\neq c(v)$ for every…
We prove that the (divisorial) gonality of a finite connected graph is lower bounded by its treewidth. We show that equality holds for grid graphs and complete multipartite graphs. We prove that the treewidth lower bound also holds for…