We present images at 6 and 14 GHz of Source I in Orion-KL. At higher frequencies, from 43 to 340 GHz, this source are dominated by thermal emission dust a 100 AU diameter circumstellar disk, but the is elongated along minor axis aligned with SiO bipolar outflow central object. Gaussian fits 6, 14, 43, 99 find component disk whose flux length vary frequency consistent free-free an ionized outflo...

A graph is called pseudo-outerplanar if each block has an embedding on the plane in such a way that the vertices lie on a fixed circle and the edges lie inside the disk of this circle with each of them crossing at most one another. In this paper, we prove that each pseudo-outerplanar graph admits edge decompositions into a linear forest and an outerplanar graph, or a star forest and an outerpla...

Markov Decision Processes (MDPs) are extremely useful for modeling and solving sequential decision making problems. Graph-based MDPs provide a compact representation for MDPs with large numbers of random variables. However, the complexity of exactly solving a graph-based MDP usually grows exponentially in the number of variables, which limits their application. We present a new variational fram...

Abstract We give a new characterisation of virtually free groups using graph minors. Namely, we prove that finitely generated, infinite group is if and only for any finite generating set, the corresponding Cayley minor excluded. This answers question Ostrovskii Rosenthal. The proof relies on showing generated excluded with respect to every set accessible, graph-theoretic accessibility due Thoma...

A monumental project in graph theory was recently completed. The project, started by Robertson and Seymour, and later joined by Thomas, led to entirely new concepts and a new way of looking at graph theory. The motivating problem was Kuratowski’s characterization of planar graphs, and a far-reaching generalization of this, conjectured by Wagner: If a class of graphs is minor-closed (i.e., it is...

The aim of this paper is to prove a Turán type theorem for random graphs. For 0 < γ ≤ 1 and graphs G and H, write G→γ H if any γ-proportion of the edges of G spans at least one copy of H in G. We show that for every l ≥ 2 and every fixed real 1/(l − 1) > δ > 0 almost every graph G in the binomial random graph model G(n, q), with q = q(n) ((logn)4/n)1/(l−1), satisfies G→(l−2)/(l−1)+δ Kl, where K...

We present sublinear-time (randomized) algorithms for finding simple cycles of length at least k ≥ 3 and tree-minors in bounded-degree graphs. The complexity of these algorithms is related to the distance of the graph from being Ck-minor free (resp., free from having the corresponding tree-minor). In particular, if the graph is Ω(1)-far from being cycle-free (i.e., a constant fraction of the ed...

In their work on graph minors, Robertson and Seymour begin by describing graphs whose structure is particularly simple, graphs that look roughly like thickened paths [ 8, 3 ]. They say that such graphs have small ‘path-width’. Of course, not every graph looks roughly like a thickened path, but it is possible to describe those that do not: every graph of large path-width contains a particular su...

For a fixed graph H, the H-Minor Edit problem takes as input a graph G and an integer k and asks whether G can be modified into H by a total of at most k edge contractions, edge deletions and vertex deletions. Replacing edge contractions by vertex dissolutions yields the H-Topological Minor Edit problem. For each problem we show polynomial-time solvable and NP-complete cases depending on the ch...

We derive precise asymptotic estimates for the number of labelled graphs not containing K3,3 as a minor, and also for those which are edge maximal. Additionally, we establish limit laws for parameters in random K3,3-minor-free graphs, like the expected number of edges. To establish these results, we translate a decomposition for the corresponding graph class into equations for generating functi...