Page 44 - Ellingham, Mark, Mariusz Meszka, Primož Moravec, Enes Pasalic, 2014. 2014 PhD Summer School in Discrete Mathematics. Koper: University of Primorska Press. Famnit Lectures, 3.
P. 44
1.9 References
→ hamilton cycle embedding of Kmt ,mt ,mt (delete first vertex class).
1.9 References
[Ar92] Dan Archdeacon, The medial graph and voltage-current duality, Discrete Math.
104 (1992) 111-141.
[BGGS00] C. P. Bonnington M. J. Grannell, T. S. Griggs and J. Širánˇ , Exponential families
of non-isomorphic triangulations of complete graphs, J. Combin. Theory Ser. B 78
(2000) 169-184.
[BL] C.Paul Bonnington and Charles H.C. Little, The Foundations of Topological Graph
Theory, Springer, 1995.
[Bo78a] A. Bouchet, Orientable and nonorientable genus of the complete bipartite graph,
J. Combin. Theory Ser. B 24 (1978) 24-33.
[Bo78b] A. Bouchet, Triangular imbeddings into surfaces of a join of equicardinal inde-
pendent sets following an Eulerian graph. Theory and applications of graphs (Proc.
Internat. Conf., Western Mich. Univ., Kalamazoo, Mich., 1976), pp. 86-115, Lecture
Notes in Math., 642, Springer, Berlin, 1978.
[Bo82] A. Bouchet, Constructions of covering triangulations with folds. J. Graph Theory
6 (1982) 57–74.
[ES12] M. N. Ellingham and Justin Z. Schroeder, Nonorientable hamilton cycle embed-
dings of complete tripartite graphs, Discrete Math. 312 (2012) 1911-1917.
[ES14a] M. N. Ellingham and Justin Z. Schroeder, Orientable hamilton cycle embeddings
of complete tripartite graphs I: latin square constructions, J. Combin. Designs 22
(2014) 71-94.
[ES14b] M. N. Ellingham and Justin Z. Schroeder, Orientable hamilton cycle embed-
dings of complete tripartite graphs II: voltage graph constructions and applications,
J. Graph Theory, to appear (available online).
[ES09] M. N. Ellingham and D. Christopher Stephens, The orientable genus of some joins
of complete graphs with large edgeless graphs, Discrete Math. 309 (2009) 1190-1198.
[ESZ06] M. N. Ellingham, Chris Stephens and Xiaoya Zha, The nonorientable genus of
complete tripartite graphs, J. Combin. Theory Ser. B 96 (2006) 529-559.
[GG08] M. J. Grannell and T. S. Griggs A lower bound for the number of triangular em-
beddings of some complete graphs and complete regular J. Combin. Theory Ser. B
98 (2008) 637-650.
[GGS98] M. J. Grannell, T. S. Griggs and J. Širánˇ , Face 2-colourable triangular embeddings
of complete graphs, J. Combin. Theory Ser. B 74 (1998) 8-19.
[GT] J. L. Gross and T. W. Tucker, Topological Graph Theory (reprint edition), Dover, Mi-
neola, NY, 2001.
[KSZ04] Ken-ichi Kawarabayashi, Chris Stephens and Xiaoya Zha, Orientable and nonori-
entable genera of some complete tripartite graphs, SIAM J. Discrete Math. 18 (2004)
479-487.
→ hamilton cycle embedding of Kmt ,mt ,mt (delete first vertex class).
1.9 References
[Ar92] Dan Archdeacon, The medial graph and voltage-current duality, Discrete Math.
104 (1992) 111-141.
[BGGS00] C. P. Bonnington M. J. Grannell, T. S. Griggs and J. Širánˇ , Exponential families
of non-isomorphic triangulations of complete graphs, J. Combin. Theory Ser. B 78
(2000) 169-184.
[BL] C.Paul Bonnington and Charles H.C. Little, The Foundations of Topological Graph
Theory, Springer, 1995.
[Bo78a] A. Bouchet, Orientable and nonorientable genus of the complete bipartite graph,
J. Combin. Theory Ser. B 24 (1978) 24-33.
[Bo78b] A. Bouchet, Triangular imbeddings into surfaces of a join of equicardinal inde-
pendent sets following an Eulerian graph. Theory and applications of graphs (Proc.
Internat. Conf., Western Mich. Univ., Kalamazoo, Mich., 1976), pp. 86-115, Lecture
Notes in Math., 642, Springer, Berlin, 1978.
[Bo82] A. Bouchet, Constructions of covering triangulations with folds. J. Graph Theory
6 (1982) 57–74.
[ES12] M. N. Ellingham and Justin Z. Schroeder, Nonorientable hamilton cycle embed-
dings of complete tripartite graphs, Discrete Math. 312 (2012) 1911-1917.
[ES14a] M. N. Ellingham and Justin Z. Schroeder, Orientable hamilton cycle embeddings
of complete tripartite graphs I: latin square constructions, J. Combin. Designs 22
(2014) 71-94.
[ES14b] M. N. Ellingham and Justin Z. Schroeder, Orientable hamilton cycle embed-
dings of complete tripartite graphs II: voltage graph constructions and applications,
J. Graph Theory, to appear (available online).
[ES09] M. N. Ellingham and D. Christopher Stephens, The orientable genus of some joins
of complete graphs with large edgeless graphs, Discrete Math. 309 (2009) 1190-1198.
[ESZ06] M. N. Ellingham, Chris Stephens and Xiaoya Zha, The nonorientable genus of
complete tripartite graphs, J. Combin. Theory Ser. B 96 (2006) 529-559.
[GG08] M. J. Grannell and T. S. Griggs A lower bound for the number of triangular em-
beddings of some complete graphs and complete regular J. Combin. Theory Ser. B
98 (2008) 637-650.
[GGS98] M. J. Grannell, T. S. Griggs and J. Širánˇ , Face 2-colourable triangular embeddings
of complete graphs, J. Combin. Theory Ser. B 74 (1998) 8-19.
[GT] J. L. Gross and T. W. Tucker, Topological Graph Theory (reprint edition), Dover, Mi-
neola, NY, 2001.
[KSZ04] Ken-ichi Kawarabayashi, Chris Stephens and Xiaoya Zha, Orientable and nonori-
entable genera of some complete tripartite graphs, SIAM J. Discrete Math. 18 (2004)
479-487.
