Sharif Digital Repository

Let G be a graph with n vertices and m edges and assume that f : V ( G ) → N is a function with ∑v ∈ V ( G ) f ( v ) = m + n. We show that, if we can assign to any vertex v of G a list Lv of size f ( v ) such that G has a unique vertex coloring with these lists, then G is f-choosable. This implies that, if ∑v ∈ V ( G ) f ( v ) > m + n, then there is no list assignment L such that | Lv | = f ( v ) for any v ∈ V ( G ) and G is uniquely L-colorable. Finally, we prove that if G is a connected non-regular multigraph with a list assignment L of edges such that for each edge e = u v, | Le | = max { d ( u ), d ( v ) }, then G is not uniquely L-colorable and we conjecture that this result holds for... 

We construct counterexamples to the conjecture of Xu (1990, J. Combin. Theory Ser. B50, 319-320) that every uniquely r-colorable graph of order n with exactly (r-1)n-(r2) edges must contain a Kr. © 2001 Academic Press  

A graph is said to be uniquely list colorable, if it admits a list assignment which induces a unique list coloring. We study uniquely list colorable graphs with a restriction on the number of colors used. In this way, we generalize a theorem which characterizes uniquely 2-list colorable graphs. We introduce the uniquely list chromatic number of a graph and make a conjecture about it which is a generalization of the well-known Brooks' theorem. © 2002 Elsevier Science B.V  

In this paper we describe some mechanical, hardware and software aspects of our robots specially used in teamwork. The pneumatic design of the gripers and kicker enables the robot to make a good control of ball when dribbling and also passing the ball in short and long distances. The teamwork software enables our robots to perform a cooperative behavior by dividing the field to three major regions and assigning each robot a role such as defender, forward and middle in these three regions. The server can order the robots to change their role when needed and make them return to their original state after a short time. © 2002 Springer-Verlag Berlin Heidelberg  

Arvand is the name of robots specially designed and con-structed by sharif CE team for playing soccer according to RoboCup rules and regulations for the middle size robots. Two different types of robots are made, players and the goal keeper. A player robot consists of three main parts: mechanics (motion mechanism and kicker), hard-ware (image acquisition, processing unit and control unit) and software (image processing, wireless communication, motion control and decision making). The motion mechanism is based on two drive unit, two steer units and a castor wheel. We designed a special control board which uses two microcontrollers to carry out the software system decisions and transfers them... 

Arvand is a robot specially designed and constructed for playing soccer according to RoboCup rules and regulations for the medium size robots. This robot consists of three main parts: mechanics (motion mechanism and kicker), hardware (image acquisition, processing unit and control unit) and software (image processing, wireless communication, motion control and decision making). The motion mechanism is based on a drive unit, a steer unit and a castor wheel. We designed a special control board which uses two microcontrollers to carry out the software system decisions and transfers them to the robot mechanics. The software system written in C++ performs real time image processing and object...