The Non-Biplanar Character of the Complete 9-Graph
- 1 September 1963
- journal article
- Published by Canadian Mathematical Society in Canadian Mathematical Bulletin
- Vol. 6 (3) , 319-330
- https://doi.org/10.4153/cmb-1963-026-x
Abstract
Let us define a planar partition of a graph G as a pair {H1, H2} of subgraphs of G with the following properties (i)Each of H1 and H2 includes all the vertices of G. (ii)Each edge of G belongs to just one of H1 and H2. (iii)H1 and H2 are planar graphs. It is not required that H1 and H2 are connected. Moreover either of these graphs may have isolated vertices, incident with none of its edges.We describe a graph having a planar partition as biplanar.Keywords
This publication has 3 references indexed in Scilit:
- A Census of Planar TriangulationsCanadian Journal of Mathematics, 1962
- Every planar graph with nine points has a nonplanar complementBulletin of the American Mathematical Society, 1962
- Sur le problème des courbes gauches en TopologieFundamenta Mathematicae, 1930