Planar Graphs: Logical Complexity and Parallel Isomorphism Tests

Details Planar Graphs: Logical Complexity and Parallel Isomorphism Tests Planar Graphs: Logical Complexity and Parallel Isomorphism Tests

2006-07-08

arxiv.org/abs/cs/0607033v1

Computer Science

Computational Complexity

36 pages

Scientific paper

We prove that every triconnected planar graph is definable by a first order
sentence that uses at most 15 variables and has quantifier depth at most
$11\log_2 n+43$. As a consequence, a canonic form of such graphs is computable
in $AC^1$ by the 14-dimensional Weisfeiler-Lehman algorithm. This provides
another way to show that the planar graph isomorphism is solvable in $AC^1$.

Affiliated with

Also associated with

No associations

Rating

Planar Graphs: Logical Complexity and Parallel Isomorphism Tests does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Planar Graphs: Logical Complexity and Parallel Isomorphism Tests, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Planar Graphs: Logical Complexity and Parallel Isomorphism Tests will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-347661