High-girth cubic graphs are homomorphic to the Clebsch graph

Details High-girth cubic graphs are homomorphic to the Clebsch graph High-girth cubic graphs are homomorphic to the Clebsch graph

2006-02-27

arxiv.org/abs/math/0602580v2

Mathematics

Combinatorics

17 pages

Scientific paper

We give a (computer assisted) proof that the edges of every graph with maximum degree 3 and girth at least 17 may be 5-colored (possibly improperly) so that the complement of each color class is bipartite. Equivalently, every such graph admits a homomorphism to the Clebsch graph. Hopkins and Staton and Bondy and Locke proved that every (sub)cubic graph of girth at least 4 has an edge-cut containing at least 4/5 of the edges. The existence of such an edge-cut follows immediately from the existence of a 5-edge-coloring as described above, so our theorem may be viewed as a coloring extension of their result (under a stronger girth assumption). Every graph which has a homomorphism to a cycle of length five has an above-described 5-edge-coloring; hence our theorem may also be viewed as a weak version of Nesetril's Pentagon Problem (which asks whether every cubic graph of sufficiently high girth is homomorphic to C_5).

Affiliated with

Also associated with

No associations

Rating

High-girth cubic graphs are homomorphic to the Clebsch graph 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 High-girth cubic graphs are homomorphic to the Clebsch graph, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and High-girth cubic graphs are homomorphic to the Clebsch graph will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-485814