Domain-specific model integrated program synthesis (MIPS) environments are created according to a modeling paradigm – a description of the class of models that can be created using the system. Just as model integrated computing applications are executable instances of domain models, domain models can be viewed as instances of meta-models. Desired modeling environment characteristics are selecte...

The competition graph of a digraph is defined to be the intersection graph of the family of the out-neighborhoods of the vertices of the digraph (see [6] for intersection graphs). A digraph D is a pair (V (D), A(D)) of a set V (D) of vertices and a set A(D) of ordered pairs of vertices, called arcs. An arc of the form (v, v) is called a loop. For a vertex x in a digraph D, we denote the out-nei...

The integer round-up 4(G) of the fractional chromatic index yields the standard lower bound for the chromatic index of a multigraph G. We show that if G has even order n, then the chromatic index exceeds 4(G) by at most max{log,,, n, 1 + n/30}. More generally, we show that for any real b, 2/3 <b < 1, the chromatic index of G exceeds 4(G) by at most max{log,,b n, 1 +n(l b)/lO}. This is used to s...

Let bp(+Kv) be the minimum number of complete bipartite subgraphs needed to partition the edge set of +Kv , the complete multigraph with + edges between each pair of its v vertices. Many papers have examined bp(+Kv) for v 2+. For each + and v with v 2+, it is shown here that if certain Hadamard and conference matrices exist, then bp(+Kv) must be one of two numbers. Also, generalizations to deco...

We define the limiting density of a minor-closed family of simple graphs F to be the smallest number k such that every n-vertex graph in F has at most kn(1+o(1)) edges, and we investigate the set of numbers that can be limiting densities. This set of numbers is countable, well-ordered, and closed; its order type is at least ωω. It is the closure of the set of densities of density-minimal graphs...

A subgraph H of a multigraph G is called strongly spanning, if any vertex of G is not isolated in H , while it is called maximum k-edge-colorable, if H is proper k-edge-colorable and has the largest size. We introduce a graph-parameter sp(G), that coincides with the smallest k that a graph G has a strongly spanning maximum k-edge-colorable subgraph. Our first result offers some alternative defi...

In this paper, we propose a new model that is capable of recognizing overlapping mentions. We introduce a novel notion of mention separators that can be effectively used to capture how mentions overlap with one another. On top of a novel multigraph representation that we introduce, we show that efficient and exact inference can still be performed. We present some theoretical analysis on the dif...

We prove that the vertex set of any twin-free loopless multigraph G has an embedding into some point set P of some Euclidean space R , such that the automorphism group of G is isomorphic to the isometry group of R globally preserving P .