Oleg Borodin and André Raspaud
"A sufficient condition for planar graphs to be 3-colorable"
Journal of Combinatorial Theory B88, 2003, 17–27
state the following conjecture:
Conjecture 1.2:
Every planar graph without adjacent 3-cycles and 5-cycles is 3-colorable.
My question is whether it is possible to describe this condition of "non-adjacent 3-cycles" purely in terms of the cubic adjacency matrix?
