The chain graph sandwich problem asks: Given a vertex set V , a mandatory edge set E1, and a larger edge set E2, is there a graph G= (V ,E) such that E1 ⊆ E ⊆ E2 with G being a chain graph (i.e., a 2K2-free bipartite graph)? We prove that the chain graph sandwich problem is NP-complete. This result stands in contrast to (1) the case where E1 is a connected graph, which has a linear-time solutio...

let $r$ be a commutative ring with identity. let $g(r)$ denote the maximal graph associated to $r$, i.e., $g(r)$ is a graph with vertices as the elements of $r$, where two distinct vertices $a$ and $b$ are adjacent if and only if there is a maximal ideal of $r$ containing both. let $gamma(r)$ denote the restriction of $g(r)$ to non-unit elements of $r$. in this paper we study the various graphi...

We describe G-Space (Geodesic Space), a straightforward linear time layout algorithm that draws undirected graphs based purely on their topological features. The algorithm is divided into two phases. The first phase is an embedding of the graph into a 2-D plane using geodesic distances as coordinates. These coordinates are computed with the same process used by HDE (High-Dimensional Embedding) ...

We study the optimal design of graph filters (GFs) to implement arbitrary linear transformations between graph signals. GFs can be represented by matrix polynomials of the graph-shift operator (GSO). Since this operator captures the local structure of the graph, GFs naturally give rise to distributed operators. In most setups the GSO is given, so that GF design consists fundamentally in choosin...

We prove that a connected graph has linear rank-width 1 if and only if it is a distance-hereditary graph and its split decomposition tree is a path. An immediate consequence is that one can decide in linear time whether a graph has linear rank-width at most 1, and give an obstruction if not. Other immediate consequences are several characterisations of graphs of linear rankwidth 1. In particula...

Assume there exists a pseudo-elliptic monoid. We wish to extend the results of [39] to meromorphic, positive, contra-everywhere open planes. We show that E = ∅. It has long been known that u < i [39]. In [39], it is shown that sF,p 6= V ′′.

Let µ 1 (G) ≥. .. ≥ µn (G) be the eigenvalues of the adjacency matrix of a graph G of order n, and G be the complement of G. Suppose F (G) is a fixed linear combination of µ i (G) , µ n−i+1 (G) , µ i G ¡ , and µ n−i+1 G ¡ , 1 ≤ i ≤ k. It is shown that the limit lim n→∞ 1 n max {F (G) : v (G) = n} always exists. Moreover, the statement remains true if the maximum is taken over some restricted fa...

This paper shows that a simple baseline based on a Bag-of-Words (BoW) representation learns surprisingly good knowledge graph embeddings. By casting knowledge base completion and question answering as supervised classification problems, we observe that modeling co-occurences of entities and relations leads to state-of-the-art performance with a training time of a few minutes using the open sour...

The paper investigates relationships between algebraic expressions and graphs. Using the decomposition method we generate special simultaneous systems of linear recurrences for sizes of graph expressions. We propose techniques which provide closed-form solutions for these systems.

Graphs are an integral data structure for many parts of computation. They are highly effective at modeling many varied and flexible domains, and are excellent for representing the way humans themselves conceive of the world. Nowadays, there is lots of interest in working with large graphs, including social network graphs, “knowledge” graphs, and large bipartite graphs (for example, the Netflix ...