Nonorientable genus of cartesian products of regular graphs

A special type of surgery developed by A. T. White and later used by the author to construct orientable quadrilateral embeddings of Cartesian products of graphs is here expanded to cover the nonorientable case as well. This enables the nonorientable genus of many families of Cartesian products of triangle-free graphs to be computed.

[1]  Jonathan L. Gross,et al.  Generating all graph coverings by permutation voltage assignments , 1977, Discret. Math..

[2]  Jonathan L. Gross,et al.  Quotients of complete graphs: revisiting the Heawood map-coloring problem. , 1974 .

[3]  Tomaz Pisanski,et al.  Dual imbeddings and wrapped quasi-coverings of graphs , 1980, Discret. Math..

[4]  Saul Stahl,et al.  Generalized Embedding Schemes , 1978, J. Graph Theory.

[5]  Saul Stahl,et al.  The embeddings of a graph - A survey , 1978, J. Graph Theory.

[6]  Anton Kotzig,et al.  1-Factorizations of cartesian products of regular graphs , 1979, J. Graph Theory.

[7]  Tomaž Pisanski.  Genus of cartesian products of regular bipartite graphs , 1980, J. Graph Theory.

[8]  Tomaz Pisanski,et al.  Edge-coloring of a family of regular graphs. , 1983 .

[9]  J. Gross,et al.  The topological theory of current graphs , 1974 .

[10]  Mark Jungerman.  The non-orientable genus of the $n$-cube. , 1978 .

[11]  Jonathan L. Gross,et al.  Voltage graphs , 1974, Discret. Math..

[12]  Gerhard Ringel,et al.  The combinatorial map color theorem , 1977, J. Graph Theory.

[13]  G. Ringel.  Über drei kombinatorische Probleme amn-dimensionalen Würfel und Würfelgitter , 1955 .

[14]  A. White.  On the genus of a group , 1972 .

[15]  Arthur T. White,et al.  ON THE GENUS OF THE COMPOSITION OF TWO GRAPHS , 1972 .

[16]  Saul Stahl,et al.  Genus embeddings for some complete tripartite graphs , 1976, Discret. Math..

[17]  Renu C. Laskar,et al.  Chromatic Numbers for Certain Graphs , 1972 .

[18]  G. Prins,et al.  Every generalized Petersen graph has a Tait coloring. , 1972 .