Information Processing Letters
Discrete Applied Mathematics
Optimal node ranking of trees in linear time
Information Processing Letters
The role of elimination trees in sparse factorization
SIAM Journal on Matrix Analysis and Applications
On an edge ranking problem of trees and graphs
Discrete Applied Mathematics
Discrete Mathematics
Edge ranking of graphs is hard
Discrete Applied Mathematics
SIAM Journal on Discrete Mathematics
Vertex ranking of asteroidal triple-free graphs
Information Processing Letters
Bandwidth and density for block graphs
Discrete Mathematics
Finding optimal edge-rankings of trees
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Optimal path cover problem on block graphs
Theoretical Computer Science
On the vertex ranking problem for trapezoid, circular-arc and other graphs
Discrete Applied Mathematics
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
On Vertex Ranking for Permutations and Other Graphs
STACS '94 Proceedings of the 11th Annual Symposium on Theoretical Aspects of Computer Science
Computational Aspects of VLSI
Vertex rankings of chordal graphs and weighted trees
Information Processing Letters
SFCS '80 Proceedings of the 21st Annual Symposium on Foundations of Computer Science
SOFSEM '10 Proceedings of the 36th Conference on Current Trends in Theory and Practice of Computer Science
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A vertex ranking of an undirected graph G is a labeling of the vertices of G with integers such that every path connecting two vertices with the same label i contains an intermediate vertex with label ji. A vertex ranking of G is called optimal if it uses the minimum number of distinct labels among all possible vertex rankings. The problem of finding an optimal vertex ranking for general graphs is NP-hard, and NP-hard even for chordal graphs which form a superclass of block graphs. In this paper, we present the first polynomial algorithm which runs in O(n^2log@D) time for finding an optimal vertex ranking of a block graph G, where n and @D denote the number of vertices and the maximum degree of G, respectively.