Labeling planar graphs with a condition at distance two

Authors:
Peter Bella;Daniel Král';Bojan Mohar;Katarína Quittnerová
Affiliations:
Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Prague, Czech Republic;Department of Applied Mathematics and Institute for Theoretical Computer Science,22Institute for Theoretical Computer Science (ITI) is supported as project 1M0545 by Ministry of Education of Czech ...;Department of Mathematics, University of Ljubljana, Jadranska19, 1000 Ljubljana, Slovenia and Department of Mathematics, Simon Fraser University, Burnaby, BC, V5A 1S6, Canada;Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Prague, Czech Republic
Venue:
European Journal of Combinatorics
Year:
2007

Citing 15
Cited 6

Labelling graphs with a condition at distance 2

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

SIAM Journal on Discrete Mathematics
The $L(2,1)$-Labeling Problem on Graphs

SIAM Journal on Discrete Mathematics
Coloring powers of planar graphs

SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
On L(d, 1)-labelings of graphs

Discrete Mathematics
L(2,1)-labeling of planar graphs

DIALM '01 Proceedings of the 5th international workshop on Discrete algorithms and methods for mobile computing and communications
Fixed parameter complexity of λ-labelings

Discrete Applied Mathematics - special issue on the 25th international workshop on graph theoretic concepts in computer science (WG'99)
Frequency Channel Assignment on Planar Networks

ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
A Theorem about the Channel Assignment Problem

SIAM Journal on Discrete Mathematics
On the span in channel assignment problems: bounds, computing and counting

Discrete Mathematics - Special issue: The 18th British combinatorial conference
Coloring Powers of Planar Graphs

SIAM Journal on Discrete Mathematics
Labeling Planar Graphs with Conditions on Girth and Distance Two

SIAM Journal on Discrete Mathematics
Coloring Powers of Chordal Graphs

SIAM Journal on Discrete Mathematics
A bound on the chromatic number of the square of a planar graph

Journal of Combinatorial Theory Series B
Coloring the square of a planar graph

Journal of Graph Theory

Distance constrained labelings of planar graphs with no short cycles

Discrete Applied Mathematics
Graph labellings with variable weights, a survey

Discrete Applied Mathematics
k-L(2,1)-labelling for planar graphs is NP-complete for k≥4

Discrete Applied Mathematics
Survey: Randomly colouring graphs (a combinatorial view)

Computer Science Review
Griggs and Yeh's Conjecture and $L(p,1)$-labelings

SIAM Journal on Discrete Mathematics
Labeling outerplanar graphs with maximum degree three

Discrete Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

An L(2,1)-labeling of a graph is a mapping c:V(G)-{0,...,K} such that the labels assigned to neighboring vertices differ by at least 2 and the labels of vertices at distance two are different. The smallest K for which an L(2,1)-labeling of a graph G exists is denoted by @l"2","1(G). Griggs and Yeh [J.R. Griggs, R.K. Yeh, Labeling graphs with a condition at distance 2, SIAM J. Discrete Math. 5 (1992) 586-595] conjectured that @l"2","1(G)@?@D^2 for every graph G with maximum degree @D=2. We prove the conjecture for planar graphs with maximum degree @D3. All our results also generalize to the list-coloring setting.