منابع مشابه
Graph Imperfection
We are interested in colouring a graph G=(V, E) together with an integral weight or demand vector x=(xv : v # V) in such a way that xv colours are assigned to each node v, adjacent nodes are coloured with disjoint sets of colours, and we use as few colours as possible. Such problems arise in the design of cellular communication systems, when radio channels must be assigned to transmitters to sa...
متن کاملGraph Imperfection II
The imperfection ratio is a graph invariant which indicates how good a lower bound the weighted clique number gives on the weighted chromatic number, in the limit as weights get large. Its introduction was motivated by investigations of the radio channel assignment problem, where one has to assign channels to transmitters and the demands for channels at some transmitters are large. In this pape...
متن کاملComparing Imperfection Ratio and Imperfection Index for Graph Classes
Perfect graphs constitute a well-studied graph class with a rich structure, reflected by many characterizations with respect to different concepts. Perfect graphs are, for instance, precisely those graphs G where the stable set polytope STAB(G) coincides with the fractional stable set polytope QSTAB(G). For all imperfect graphs G it holds that STAB(G) ⊂ QSTAB(G). It is, therefore, natural to us...
متن کاملGraph imperfection and channel assignment
Given a graph G and a non-negative integer weight or demand xv for each node v, a colouring of the pair (G, x) is an assignment to each node v of a set of xv colours such that adjacent nodes receive disjoint sets of colours. We are interested in such colourings when the maximum demand xv is large. An application where such colouring problems arise is in the design of cellular radio communicatio...
متن کاملGraph Imperfection with a Co-Site Constraint
We are interested in a version of graph colouring where there is a ‘co-site’ constraint value k. Given a graph G with a non-negative integral demand xv at each node v, we must assign xv positive integers (colours) to each node v such that the same integer is never assigned to adjacent nodes, and two distinct integers assigned to a single node differ by at least k. The aim is to minimise the spa...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2001
ISSN: 0095-8956
DOI: 10.1006/jctb.2001.2042