Information Processing Letters
The role of elimination trees in sparse factorization
SIAM Journal on Matrix Analysis and Applications
Approximating treewidth, pathwidth, frontsize, and shortest elimination tree
Journal of Algorithms
Discrete Mathematics
SIAM Journal on Discrete Mathematics
Online Conflict-Free Coloring for Intervals
SIAM Journal on Computing
SFCS '80 Proceedings of the 21st Annual Symposium on Foundations of Computer Science
Deterministic conflict-free coloring for intervals: From offline to online
ACM Transactions on Algorithms (TALG)
Conflict-Free colorings of rectangles ranges
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
The potential to improve the choice: list conflict-free coloring for geometric hypergraphs
Proceedings of the twenty-seventh annual symposium on Computational geometry
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We investigate the relationship between two kinds of vertex colorings of graphs: unique-maximum colorings and conflict-free colorings. In a unique-maximum coloring, the colors are ordered, and in every path of the graph the maximum color appears only once. In a conflict-free coloring, in every path of the graph there is a color that appears only once. We also study computational complexity aspects of conflict-free colorings and prove a completeness result. Finally, we improve lower bounds for those chromatic numbers of the grid graph.