Loading...
| Friend's email | |
| Your name | |
| Your email | |
| enter code | |
This page was sent successfuly
- Type of Document: Ph.D. Dissertation
- Language: Farsi
- Document No: 48457 (02)
- University: Sharif University of Technology
- Department: Mathematical Sciences
- Advisor(s): Daneshgar, Amir
- Abstract:
- In this thesis we introduce the cylindrical construction, and show that a large number of well-known graph constructions are cylindrical. Then, we prove a tensor-hom duality for this construction and its dual as factors. These fanctors, introduce a reduction from graphs to labeled ones, which is usefull to prove (non-)existance of homomorphisms. By using such reductions,we solve some homomorphism problems from generalized Grotzsch, generalized Petersen-like and Coxeter-like graphs to cycles. Then, we introduce tree cylinders and using them we introduce constructions with smaller maximum degree that do not reduce the girth and odd girth, but preserves homomorphism properties of the given graph. Also, we introduce an approach usefull to find the odd girth of some graph classess such as circulant, generalized Petersen and generalized Coxeter graphs. To do this, we show that finding the odd girth is equialent to solving an integer program. As an example, we calculate the odd girth of generalized Petersen graphs, explicitely. Knowing the odd girth will be applied to find some (no-)homomorphism problems and bounds for circular chromatic number of these graphs
- Keywords:
- Integer Programming ; Cylindrical Construction ; Graph Homomorphism ; Generalized Petersen Graphs ; Graph Labeling ; Extremal Limit ; Pentagon Problem
Digital Object List
-
محتواي کتاب
- view
Bookmark