Exponential families of nonisomorphic nonorientable genus embeddings of complete
graphs Page 1 http://www.elsevier.com/locate/jctb Journal of Combinatorial Theory, Series …

A longstanding open question of Archdeacon and Craft asks whether every complete graph
has a minimum genus embedding with at most one nontriangular face. We exhibit such an …

Constructions due to Ringel show that there exists a nonorientable face 2-colourable
triangular embedding of the complete graph on n vertices (equivalently a nonorientable …

We show that for n= 4 and n⩾ 6, Kn has a nonorientable embedding in which all the facial
walks are hamilton cycles. Moreover, when n is odd there is such an embedding that is 2 …

We give a more simple proof of the Map Color Theorem for nonorientable surfaces that uses
only four constructions of current graphs instead of 12 constructions used in the previous …

It is known that for all sufficiently large s, there are at least article\footskip= 0pc empty (53) 2s
nonequivalent graceful labellings of the path on 2s+ 1 vertices. Using this result, we …

We describe a linear-time algorithm for 4-coloring planar graphs. We indeed give an O (V+
E+| χ|+ 1)-time algorithm to C-color V-vertex E-edge graphs embeddable on a 2-manifold M …