Book ChapterDOI
Hole: An Emerging Character in the Story of Radio k-Coloring Problem
Ushnish Sarkar,Avishek Adhikari +1 more
- pp 3-41
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TLDR
This chapter highlights many combinatorial aspects of holes in the context of radio k-coloring problem and its applicability as well as importance in real life.Abstract:
Frequency assignment problem (FAP) of radio networks is a very active area of research. In this chapter, radio networks have been studied in a graph-theoretic approach where the base stations of a cellular network are vertices and two vertices are adjacent if the corresponding stations transmit or receive broadcast of each other. Here, we deal with the problem of allocating frequencies to the base stations of the cellular network such that interference between stations at different distances can be avoided and at the same time, and the range of distinct frequencies used can be kept minimum. A certain variant of FAP on such network is radio k-coloring problem (\(k\ge 2\) being a positive integer) where stations (vertices) are assigned frequencies (colors) in such a way that the frequency difference increases (using k as a parameter) with the growing proximity of the stations. The focus has been laid on unused frequencies in the spectrum. These unused frequencies are referred as holes, and they are found to heavily influence the structure of the network (graph). In this chapter, we highlight many combinatorial aspects of holes in the context of radio k-coloring problem and its applicability as well as importance in real life.read more
References
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Book
Introduction to Graph Theory
TL;DR: In this article, the authors introduce the concept of graph coloring and propose a graph coloring algorithm based on the Eulers formula for k-chromatic graphs, which can be seen as a special case of the graph coloring problem.
Book
Fundamentals of domination in graphs
TL;DR: Bounds on the domination number domination, independence and irredundance efficiency, redundancy and the duals changing and unchanging domination conditions on the dominating set varieties of domination multiproperty and multiset parameters sums and products of parameters dominating functions frameworks for domination domination complexity and algorithms are presented.
Journal ArticleDOI
Frequency assignment: Theory and applications
TL;DR: This paper introduces the minimum-order approach to frequency assignment and presents a theory which relates this approach to the traditional one, and shows that many frequency assignment problems are equivalent to generalized graph coloring problems.
Journal ArticleDOI
Labelling graphs with a condition at distance 2
TL;DR: Given a simple graph G and a positive number d, an L_d ( 2,1 )-labelling of G is a function f:V ( G ) to [ 0,fty ) such that whenever x,y are adjacent, f ( x ) - f ( ...
Journal ArticleDOI
A note on Hamiltonian circuits
Vašek Chvátal,Paul Erdös +1 more
TL;DR: G is s-connected and has no Hamiltonian circuit, but there are s paths starting at x and terminating in C which are pairwise disjoint apart from x and share with C just their terminal vertices.