Labelling graphs with a condition at distance 2
SIAM Journal on Discrete Mathematics
Good and semi-strong colorings of oriented planar graphs
Information Processing Letters
Colorings and girth of oriented planar graphs
Proceedings of an international symposium on Graphs and combinatorics
Labeling trees with a condition at distance two
Discrete Mathematics
The 2-dipath chromatic number of Halin graphs
Information Processing Letters
A bound on the chromatic number of the square of a planar graph
Journal of Combinatorial Theory Series B
Distance-two labelings of digraphs
Discrete Applied Mathematics
Coloring the square of a planar graph
Journal of Graph Theory
Discrete Applied Mathematics
The Computer Journal
The L(2, 1)-Labeling Problem on Oriented Regular Grids
The Computer Journal
| Hi-index | 0.04 |
The L(2,1)-labeling of a digraph D is a function l from the vertex set of D to the set of all nonnegative integers such that |l(x)-l(y)|=2 if x and y are at distance 1, and l(x)l(y) if x and y are at distance 2, where the distance from vertex x to vertex y is the length of a shortest dipath from x to y. The minimum over all the L(2,1)-labelings of D of the maximum used label is denoted @l-(D). If C is a class of digraphs, the maximum @l-(D), over all D@?C is denoted @l-(C). In this paper we study the L(2,1)-labeling problem on oriented planar graphs providing some upper bounds on @l-. Then we focus on some specific subclasses of oriented planar graphs, improving the previous general bounds. Namely, for oriented prisms we compute the exact value of @l-, while for oriented Halin graphs and cacti we provide very close upper and lower bounds for @l-.