Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-20T16:24:40.332Z Has data issue: false hasContentIssue false

Trees in Polyhedral Graphs

Published online by Cambridge University Press:  20 November 2018

David Barnette*
Affiliation:
University of Washington, Seattle
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A graph is said to be d-polyhedral provided it is isomorphic with the graph formed by the vertices and edges of a d-dimensional bounded (convex) polyhedron (d-polyhedron). A k-tree is a connected acyclic graph in which each vertex is of valence ⩽k.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1966

References

1. Brown, T. A., Simple paths on convex polyhedra, Pacific J. Math., 11 (1961), 12111214.Google Scholar
2. Brown, T. A., Hamiltonian paths on convex polyhedra (unpublished note P-2069, The Rand Corporation, Santa Monica, Calif., 1960).Google Scholar
3. Dirac, G. A., Some theorems on abstract graphs, Proc. London Math. Soc, (3), 2 (1952), 6981.Google Scholar
4. Dirac, G. A., Connectivity theorems for graphs, Quart. J. Math. Oxford Ser. (2), 3 (1952), 171174.Google Scholar
5. Gale, D., Neighborly and cyclic polytopes, Proc. Symp. Pure Math., 7, Convexity (Providence, R.I., 1963), 225232.Google Scholar
6. Grünbaum, B., Steinitz's characterization of convex polyhedra in E3 (hectographed notes, University of Washington, 1963).Google Scholar
7. Grünbaum, B. and Motzkin, T. S., Longest simple paths in polyhedral graphs, J. London Math. Soc, 37 (1962), 152160.Google Scholar
8. Grünbaum, B. and Motzkin, T. S., On polyhedral graphs, Proc. Symp. Pure Math., 7, Convexity (Providence, R.I., 1963), 285290.Google Scholar
9. Moon, J. W. and Moser, L., Simple paths on polyhedra, Pacific J. Math., 13 (1963), 629631.Google Scholar
10. Steinitz, E. and Rademacher, H., Vorlesungen über die Theorie der Polyeder, (Berlin, 1934).Google Scholar