L(2,1)-labeling of planar graphs

Authors:
Tiziana Calamoneri;Rossella Petreschi
Affiliations:
Department of Computer Science, University of Rome 'La Sapienza', Italy, via Salaria 113, 00198 Roma, Italy;Department of Computer Science, University of Rome 'La Sapienza', Italy, via Salaria 113, 00198 Roma, Italy
Venue:
DIALM '01 Proceedings of the 5th international workshop on Discrete algorithms and methods for mobile computing and communications
Year:
2001

Citing 6
Cited 3

Distributed Nodes Organization Algorithm for Channel Access in a Multihop Dynamic Radio Network

IEEE Transactions on Computers
Labelling graphs with a condition at distance 2

SIAM Journal on Discrete Mathematics
Labeling Chordal Graphs: Distance Two Condition

SIAM Journal on Discrete Mathematics
Code assignment for hidden terminal interference avoidance in multihop packet radio networks

IEEE/ACM Transactions on Networking (TON)
The $L(2,1)$-Labeling Problem on Graphs

SIAM Journal on Discrete Mathematics
Assigning codes in wireless networks: bounds and scaling properties

Wireless Networks

On the Radiocoloring Problem

IWDC '02 Proceedings of the 4th International Workshop on Distributed Computing, Mobile and Wireless Computing
L(2, 1)-Coloring Matrogenic Graphs

LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
Labeling planar graphs with a condition at distance two

European Journal of Combinatorics

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper we prove a conjecture left open by Bodlaender et al. [3] concerning L(2, 1)-labeling of outerplanar graphs. L(2, 1)-labeling is a coloring problem arising from frequency assignment in multihop radio networks, in which adjacent nodes must receive colors that are at least two apart while nodes at distance two must receive different colors. Namely, we improve the best known upper bound from &Dgr; + 9 to &Dgr; + 3 colors, &Dgr; being the maximum degree of the graph and &Dgr; ⪈ 8. Consequently, we improve the additive term for triangulated outerplanar graphs from &Dgr; + 7 to &Dgr; + 2, and for planar graphs from 3&Dgr; + 29 to 3&Dgr; + 8. We also make a step towards the improvement of the factor 3 in the bound of planar graphs; in fact we prove that for hamiltonian planar graphs 2&Dgr; + 6 colors are sufficient.