Optimal edge ranking of trees in linear time
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
On Minimum Edge Ranking Spanning Trees
MFCS '99 Proceedings of the 24th International Symposium on Mathematical Foundations of Computer Science
Minimum Edge Ranking Spanning Trees of Threshold Graphs
ISAAC '02 Proceedings of the 13th International Symposium on Algorithms and Computation
An optimal parallel algorithm for c-vertex-ranking of trees
Information Processing Letters
Vertex rankings of chordal graphs and weighted trees
Information Processing Letters
Minimum edge ranking spanning trees of split graphs
Discrete Applied Mathematics - Special issue: Discrete algorithms and optimization, in honor of professor Toshihide Ibaraki at his retirement from Kyoto University
Discrete Applied Mathematics - Special issue: Discrete algorithms and optimization, in honor of professor Toshihide Ibaraki at his retirement from Kyoto University
Constructing a minimum height elimination tree of a tree in linear time
Information Sciences: an International Journal
A polynomial time algorithm for obtaining minimum edge ranking on two-connected outerplanar graphs
Information Processing Letters
Easy and hard instances of arc ranking in directed graphs
Discrete Applied Mathematics
Optimal vertex ranking of block graphs
Information and Computation
Minimal k-rankings and the rank number of Pn2
Information Processing Letters
SOFSEM '10 Proceedings of the 36th Conference on Current Trends in Theory and Practice of Computer Science
An optimal parallel algorithm for c-vertex-ranking of trees
Information Processing Letters
Vertex rankings of chordal graphs and weighted trees
Information Processing Letters
Information Processing Letters
Greedy algorithms for generalized k-rankings of paths
Information Processing Letters
Graph unique-maximum and conflict-free colorings
Journal of Discrete Algorithms
Max-optimal and sum-optimal labelings of graphs
Information Processing Letters
Forbidden graphs for tree-depth
European Journal of Combinatorics
Graph unique-maximum and conflict-free colorings
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
Unique-maximum and conflict-free coloring for hypergraphs and tree graphs
SOFSEM'12 Proceedings of the 38th international conference on Current Trends in Theory and Practice of Computer Science
Ordered coloring of grids and related graphs
Theoretical Computer Science
LIFO-search: A min-max theorem and a searching game for cycle-rank and tree-depth
Discrete Applied Mathematics
Effective computation of immersion obstructions for unions of graph classes
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
Finding the edge ranking number through vertex partitions
Discrete Applied Mathematics
Effective computation of immersion obstructions for unions of graph classes
Journal of Computer and System Sciences
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A vertex (edge) coloring $\phi:V\rightarrow \{1,2,\ldots ,t\}$ ($\phi':E\rightarrow \{1,2,\ldots,$ $t\}$) of a graph G=(V,E) is a vertex (edge) t-ranking if, for any two vertices (edges) of the same color, every path between them contains a vertex (edge) of larger color. The {\em vertex ranking number} $\chi_{r}(G)$ ({\em edge ranking number} $\chi_{r}'(G)$) is the smallest value of t such that G has a vertex (edge) t-ranking. In this paper we study the algorithmic complexity of the {\sc Vertex Ranking} and {\sc Edge Ranking} problems. It is shown that $\chi_{r}(G)$ can be computed in polynomial time when restricted to graphs with treewidth at most k for any fixed k. We characterize the graphs where the vertex ranking number $\chi_{r}$ and the chromatic number $\chi$ coincide on all induced subgraphs, show that $\chi_{r}(G)=\chi (G)$ implies $\chi (G)=\omega (G)$ (largest clique size), and give a formula for $\chi_{r}'(K_n)$.