Parallel tree contraction part 2: further applications
SIAM Journal on Computing
Proceedings of the 30th IEEE symposium on Foundations of computer science
Fixed-Point Logics on Planar Graphs
LICS '98 Proceedings of the 13th Annual IEEE Symposium on Logic in Computer Science
How complex are random graphs in first order logic?
Random Structures & Algorithms - Proceedings of the Eleventh International Conference "Random Structures and Algorithms," August 9—13, 2003, Poznan, Poland
The first order definability of graphs: upper bounds for quantifier depth
Discrete Applied Mathematics
Testing graph isomorphism in parallel by playing a game
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Decidable relationships between consistency notions for constraint satisfaction problems
CSL'09/EACSL'09 Proceedings of the 23rd CSL international conference and 18th EACSL Annual conference on Computer science logic
Fixed-point definability and polynomial time on chordal graphs and line graphs
Fields of logic and computation
Fixed-point definability and polynomial time on graphs with excluded minors
Journal of the ACM (JACM)
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We prove that every triconnected planar graph on n vertices is definable by a first order sentence that uses at most 15 variables and has quantifier depth at most 11 log2 n + 45. As a consequence, a canonic form of such graphs is computable in AC1 by the 14-dimensional Weisfeiler-Lehman algorithm. This gives us another AC1 algorithm for the planar graph isomorphism.