considering the major change occurred in business cells from plant to “chain” and the critical need to choose the best partners to form the supply chain for competing in today’s business setting, one of the vital decisions made at the early steps of constructing a business is supplier selection. given the fact that the early decisions are inherently strategic and therefore hard and costly to ch...

2. Introduction 3 2.1. Notations and conventions . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2. Simple graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3. Drawing graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.4. A first fact: The Ramsey number R (3, 3) = 6 . . . . . . . . . . . . . . 11 2.5. Degrees . . . . . . . . . . . . . . . . . ....

In this paper, we propose a new type of graph, denoted as ”embedded-graph”, and its theory, which employs a distributed representation to describe the relations on the graph edges. Embedded-graphs can express linguistic and complicated relations, which cannot be expressed by the existing edge-graphs or weighted-graphs. We introduce the mathematical definition of embedded-graph, translation, edg...

Assignment 1 François Séguin Question 1 (a) We know that for any simple graph X, v∈V (X) d(v) = 2 |E(X)|. In particular, the sum must be even. Here, summing over all the degrees of the vertices yield a total degree of 41, which is odd. Therefore, there is no such simple graph. The Handshake Lemma for bipartite graphs states that, if A and B are the disjoint independent set of vertices of the gr...

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...

We present an alternative domain concerning mathematics to investigate universal evolution mechanisms by focusing on large cycles theory (LCT)-a simplified version of well-known hamiltonian graph theory. LCT joins together a number of N P-complete cycle problems in graph theory. N P-completeness is the kay factor insuring (by conjecture of Cook) the generation of endless developments and great ...