We announce a new language resource for research on semantic parsing, a large, carefully curated collection of semantic dependency graphs representing multiple linguistic traditions. This resource is called SDP 2016 and provides an update and extension to previous versions used as Semantic Dependency Parsing target representations in the 2014 and 2015 Semantic Evaluation Exercises (SemEval). Fo...

Network reliability is an important issue in the area of distributed computing. Most of the early work in this area takes a probabilistic approach to the problem. However, sometimes it is important to incorporate subjective reliability estimates into the measure. To serve this goal, we propose the use of the weighted integrity, a measure of graph vulnerability. The weighted integrity problem is...

The independence polynomial of a graph G is the function i(G, x) = ∑k≥0 ik xk , where ik is the number of independent sets of vertices in G of cardinality k. We prove that real roots of independence polynomials are dense in (−∞, 0], while complex roots are dense in C, even when restricting to well covered or comparability graphs. Throughout, we exploit the fact that independence polynomials are...

For given finite (unordered) graphs G and H, we examine the existence of a Ramsey graph F for which the strong Ramsey arrow F −→ (G)r holds. We concentrate on the situation when H is not a complete graph. The set of graphs G for which there exists an F satisfying F −→ (G)2 2 (P2 is a path on 3 vertices) is found to be the union of the set of chordal comparability graphs together with the set of...

A graph on n vertices which is the union of two comparability graphs on the same vertex set, always contains a clique or independent set of size n 1 3 . On the other hand, there exist such graphs for which the largest clique and independent set are of size at most n. Similar results are obtained for graphs which are a union of a fixed number k of comparability graphs. We also show that the same...

We study the eigenspace with largest eigenvalue of the Laplacian matrix of a simple graph. We find a surprising connection of this space with the theory of modular decomposition of Gallai, whereby eigenvectors can be used to discover modules. In the case of comparability graphs, eigenvectors are used to induce orientations of the graph, and the set of these induced orientations is shown to (rec...

We study the eigenspace with largest eigenvalue of the Laplacian matrix of a simple graph. We find a surprising connection of this space with the theory of modular decomposition of Gallai, whereby eigenvectors can be used to discover modules. In the case of comparability graphs, eigenvectors are used to induce orientations of the graph, and the set of these induced orientations is shown to (rec...

We are interested in a version of graph colouring where there is a ‘co-site’ constraint value k. Given a graph G with a non-negative integral demand xv at each node v, we must assign xv positive integers (colours) to each node v such that the same integer is never assigned to adjacent nodes, and two distinct integers assigned to a single node differ by at least k. The aim is to minimise the spa...

Let G be a chordal graph, X(G) the complement of the associated complex arrangement and Γ(G) the fundamental group of X(G). We show that Γ(G) is a limit of colored braid groups over the poset of simplices of G. When G = GT is the comparability graph associated with a rooted tree T , a case recently investigated by the first author, the result takes the following very simple form: Γ(GT ) is a li...