Chromatic numbers of 6-regular graphs on the Klein bottle

نویسندگان

Atsuhiro Nakamoto

Norihito Sasanuma

چکیده

In this paper, we determine chromatic numbers of all 6-regular loopless graphs on the Klein bottle. As a consequence, it follows that every simple 6-regular graph on the Klein bottle is 5-colorable.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Small snarks and 6-chromatic triangulations on the Klein bottle

It is known that for every nonorientable surface there are infinitely many (large) snarks that can be polyhedrally embedded on that surface. We take a dual approach to the embedding of snarks on the Klein bottle, and investigate edge-colorings of 6-chromatic triangulations of the Klein bottle. In the process, we discover the smallest snarks that can be polyhedrally embedded on the Klein bottle....

متن کامل

Coloring Eulerian Triangulations of the Klein Bottle

We show that an Eulerian triangulation of the Klein bottle has chromatic number equal to six if and only if it contains a complete graph of order six, and it is 5-colorable, otherwise. As a consequence of our proof, we derive that every Eulerian triangulation of the Klein bottle with facewidth at least four is 5-colorable.

متن کامل

On the restricted matching extension of graphs on the torus and the Klein bottle

Aldred and Plummer proved that every 6-connected even graph minimally embedded on the torus or the Klein bottle is E(1, n)(n ≤ 3) and E(0, n)(n ≤ 5) [R.E.L. Aldred, M.D. Plummer, Restricted matching in graphs of small genus, Discrete Math. 308 (2008) 5907–5921]. In this paper, we can remove the upper bounds on n by showing that every even 6-regular graph G embedded on the torus or the Klein bot...

متن کامل

Incidence dominating numbers of graphs

In this paper, the concept of incidence domination number of graphs is introduced and the incidence dominating set and the incidence domination number of some particular graphs such as paths, cycles, wheels, complete graphs and stars are studied.

متن کامل