Here you will find code (in C++ and Python) for different unsolved problems related to cycle double cover conjecture.
How to run experiments:
./run_experiments mc < ../../multicode/Generated_graphs.10.05.sn.cyc4
How to render .png file from .dot:
neato -Tpng graph20g2-3.dot -o graph20g2-3.png
- Cycle double cover conjecture
- 5-flow conjecture
- The Berge-Fulkerson conjecture
- (m,n)-cycle covers
- Unit vector flows
- The three 4-flows conjecture
- (brand new!) oriented 6-cycle 4-cover conjecture (o6c4c, we can also call it as 'oriented Berge-Fulkerson') (what's new here is just the 'oriented' part; verified for all cyclically 4-edge-connected snarks (with girth >= 5) upto and including 30 vertices)
- oriented 5-cycle double cover conjecture (o5cdc)
- strong Petersen colouring conjecture
- oriented 9-cycle 6-cover conjecture (o9c6c) (but not for Petersen graph, because it doesn't have any 9-cycle 6-cover and it's kind of easy to understand why (TODO: write the proof): any solution for 9c6c consists of 9 layers, which are complementary to perfect matchings; if we go the complementary problem then it says that we need to cover the graph with 9 perfect matchings which cover the graph 3 times; we have 6 different perfect matchings for Petersen graph (which are all used in o6c4c solution), and each edge lies in exactly 2 of them; if we don't use any one of the perfect matchings, then we must use some of them 3 times, which is problematic (because we already cover 5 edges 3 times with it, we are left with 10 edges and no perfect matchings which can cover them); which means that 3 of perfect matchings are used once and 3 of them are used twice which means that there are some edges which are covered 2 or 4 times)
- investigations into common nowhere-zero 5-flows which come from 2BMs, 3BMs, o5cdc, o6c4c
- code for conjectures related to signed graphs - Bouchet's 6-flow conjecture
See the LICENSE file for license rights and limitations (MIT).
