Abstract
LetG be a graph embedded in a surface of genusg. It is shown that if the face-width of the embedding is at leastclog(g)/loglog(g), then such an embedding is unique up to Whitney equivalence. If the face-width is at leastclog(g), then every embedding ofG which is not Whitney equivalent to our embedding has strictly smaller Euler characteristic.
Similar content being viewed by others
References
D. Archdeacon: Densely embedded graphs,J. Combin. Theory. Ser. B.54 (1992), 13–36.
J. A. Bondy, andU. S. R. Murty:Graph Theory with Applications, North-Holland, New York, 1981.
J. L. Gross, andT. W. Tucker:Topological Graph Theory, Wiley-Interscience, New York, 1987.
B. Mohar: Combinatorial local planarity and the width of graph embeddings,Canad. J. Math.,44 (1992), 1272–1288.
N. Robertson, andR. P. Vitray: Representativity of surface embeddings, in:Paths, Flows, and VLSI-Layout, (B. Korte, L. Lovász, H. J. Prömel, and A. Schrijver Eds.), Springer-Verlag, Berlin, 1990, 293–328.
P. D. Seymour, andR. Thomas: Uniqueness of highly representative surface embeddings, preprint, 1993/94.
C. Thomassen: Embeddings of graphs with no short noncontractible cycles,J. Combin. Theory, Ser. B,48 (1990), 155–177.
W. T. Tutte: How to draw a graph,Proc. London Math. Soc.,13 (1963), 743–768.
H. Whitney: 2-isomorphic graphs,Amer. Math. J.,55 (1933), 245–254.
Author information
Authors and Affiliations
Additional information
Supported in part by the Ministry of Science and Technology of Slovenia, Research Project P1-0210-101-94.
Rights and permissions
About this article
Cite this article
Mohar, B. Uniqueness and minimality of large face-width embeddings of graphs. Combinatorica 15, 541–556 (1995). https://doi.org/10.1007/BF01192526
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01192526