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A lower bound technique for radio kappa-coloring

Das, Sandip and Ghosh, Sasthi C and Nandi, Soumen and Sen, Sagnik (2017) A lower bound technique for radio kappa-coloring. In: DISCRETE MATHEMATICS, 340 (5). pp. 855-861.

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Official URL: http://dx.doi.org/10.1016/j.disc.2016.12.021

Abstract

An n-radio k-coloring of a graph G is a function 1 : V(G) -> {0, 1, . . . , n} satisfying the condition vertical bar l(u) l(nu)vertical bar >= k + 1 - d(u, nu) for all distinct u, nu is an element of V(G). The radio k -chromatic number rc(k)(G) of G is the minimum n such that G admits an n-radio k-coloring. We establish a general technique for computing the lower bound for rc(k)(G) of a general graph G and derive a formula for it. Using this formula we compute lower bounds of rc(k)(G) for several graphs and provide alternative short proofs for a number of previously established tight lower bounds. In particular, we progress on a conjecture by Kchikech, Khentioufa and Togni (DMGT 2007) regarding rc(k)(.) of infinite paths and reprove a result by Liu and Zhu (SIDMA 2005). We also provide a 4/3-approximation algorithm for radio labeling regular grid graph of degree 6. (C) 2017 Elsevier B.V. All rights reserved.

Item Type: Journal Article
Additional Information: Copy right for this article belongs to the ELSEVIER SCIENCE BV, PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: Id for Latest eprints
Date Deposited: 20 May 2017 04:12
Last Modified: 20 May 2017 04:12
URI: http://eprints.iisc.ac.in/id/eprint/56837

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