An introduction to chromatic sums
CSC '89 Proceedings of the 17th conference on ACM Annual Computer Science Conference
On a graph partition problem with application to VLSI layout
Information Processing Letters
On chromatic sums and distributed resource allocation
Information and Computation
SIAM Journal on Discrete Mathematics
Vertex ranking of asteroidal triple-free graphs
Information Processing Letters
Discrete Applied Mathematics
SFCS '80 Proceedings of the 21st Annual Symposium on Foundations of Computer Science
Minimal k-rankings and the rank number of Pn2
Information Processing Letters
Greedy rankings and arank numbers
Information Processing Letters
| Hi-index | 0.89 |
Given a graph G, a function f:V(G)-{1,2,...,k} is a k-ranking of G if f(u)=f(v) implies that every u-v path contains a vertex w such that f(w)f(u). A k-ranking is minimal if the reduction of any label greater than 1 violates the described ranking property. We consider two norms for minimal rankings. The max-optimal norm @?f(G)@?"~ is the smallest k for which G has a minimal k-ranking. This value is also referred to as the rank number @g"r(G). In this paper we introduce the sum-optimal norm @?f(G)@?"1 which is the minimum sum of all labels over all minimal rankings. We investigate similarities and differences between the two norms. In particular we show rankings for paths and cycles that are sum-optimal are also max-optimal.