On the average genus of a graph

DOI10.1007/BF02988301zbMath0777.05051OpenAlexW2055925608MaRDI QIDQ2366954

Jonathan L. Gross, E. Ward Klein, Robert G. Rieper

Publication date: 11 August 1993

Published in: Graphs and Combinatorics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02988301

zbMATH Keywords

imbeddingsrandom variablenecklaceaverage genus

Mathematics Subject Classification ID

Planar graphs; geometric and topological aspects of graph theory (05C10)

Related Items (12)

Stratified graphs for imbedding systems ⋮ Unnamed Item ⋮ Maximum genus and connectivity ⋮ A tight lower bound on the maximum genus of a simplicial graph ⋮ Log-concavity of genus distributions of ring-like families of graphs ⋮ New bounds for the average genus and average number of faces of a simple graph ⋮ Limit points for average genus. I: 3-connected and 2-connected simplicial graphs ⋮ Remarks on the lower bounds for the average genus ⋮ The total embedding distributions of cacti and necklaces ⋮ The average genus for bouquets of circles and dipoles ⋮ Lower bounds on the maximum genus of loopless multigraphs ⋮ Overlap matrices and total imbedding distributions

Cites Work

• Region distributions of graph embeddings and Stirling numbers
• Limit points for average genus. I: 3-connected and 2-connected simplicial graphs
• Genus distributions for two classes of graphs
• An upper bound for the average number of regions
• How to determine the maximum genus of a graph
• Genus distributions for bouquets of circles
• Hierarchy for imbedding-distribution invariants of a graph
• Enumerating 2-Cell Imbeddings of Connected Graphs
• Counting Cycles in Permutations by Group Characters, With an Application to a Topological Problem
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