论文信息 - Obstruction Sets for Outer-Projective-Planar Graphs

Obstruction Sets for Outer-Projective-Planar Graphs

A graph G is outer projective planar if it can be embedded in the projective plane so that every vertex appears on the boundary of a single face We exhibit obstruction sets for outer projective planar graphs with respect to the subdivision minor and Y orderings Equivalently we nd the minimal non outer projective planar graphs under these orderings

[1] C. Kuratowski. Sur le problème des courbes gauches en Topologie , 1930 .

[2] K. Wagner. Über eine Eigenschaft der ebenen Komplexe , 1937 .

[3] J. Boland,et al. Embedding of graphs in the projective plane , 1965 .

[4] F. Harary,et al. Planar Permutation Graphs , 1967 .

[5] Gerald Berman. Frequently cited publications in pure graph theory , 1977, J. Graph Theory.

[6] Henry H. Glover,et al. 103 Graphs that are irreducible for the projective plane , 1979, J. Comb. Theory, Ser. B.

[7] Dan Archdeacon,et al. A Kuratowski theorem for the projective plane , 1981, J. Graph Theory.

[8] R. Bodendiek,et al. Die Minimalbasis der Menge aller nicht in die projektive Ebene einbettbaren Graphen. , 1981 .

[9] Walter Vollmerhaus,et al. ON COMPUTING ALL MINIMAL GRAPHS THAT ARE NOT EMBEDDABLE INTO THE PROJECTIVE PLANEPART 1 , 1986 .

[10] Paul D. Seymour,et al. Graph minors. VIII. A kuratowski theorem for general surfaces , 1990, J. Comb. Theory, Ser. B.

[11] Alexander Schrijver,et al. Disjoint homotopic paths and trees in a planar graph , 1991, Discret. Comput. Geom..

[12] Nathaniel Dean,et al. On obstructions to small face covers in planar graphs , 1992, J. Comb. Theory, Ser. B.