Labelling graphs with a condition at distance 2
SIAM Journal on Discrete Mathematics
Labeling Planar Graphs with Conditions on Girth and Distance Two
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 squares of planar graphs with girth six
European Journal of Combinatorics
Coloring the square of a planar graph
Journal of Graph Theory
Labelling planar graphs without 4-cycles with a condition on distance two
Discrete Applied Mathematics
Distance constrained labelings of planar graphs with no short cycles
Discrete Applied Mathematics
Graph labellings with variable weights, a survey
Discrete Applied Mathematics
Griggs and Yeh's Conjecture and $L(p,1)$-labelings
SIAM Journal on Discrete Mathematics
Labeling Planar Graphs without 4,5-Cycles with a Condition on Distance Two
SIAM Journal on Discrete Mathematics
| Hi-index | 0.04 |
Wegner conjectured that for each planar graph G with maximum degree @D at least 4, @g(G^2)@?@D+5 if 4@?@D@?7, and @g(G^2)@?@?3@D2@?+1 if @D=8. Let G be a planar graph without 4-cycles. In this paper, we discuss the L(p,q)-labelling of G, and show that @l"p","q(G)@?(2q-1)@D+8p+14q-11, where p and q are positive integers with p=q. As a corollary, @g(G^2)@?@D+12 and @l"2","1(G)@?@D+19.