Graphs and Combinatorics

, Volume 21, Issue 4, pp 421–425

Structural Remarks on Bipartite Graphs with Unique f-Factors


DOI: 10.1007/s00373-005-0631-2

Cite this article as:
Hoffmann, A. & Volkmann, L. Graphs and Combinatorics (2005) 21: 421. doi:10.1007/s00373-005-0631-2


In this note we will derive some structural results for a bipartite graph G with a unique f-factor. Two necessary conditions will be that G is saturated, meaning that the addition of any edge leads to a second f-factor, and that fA, fB≥1. Here fA and fB are defined as the minimum of f over the vertices in the two partite sets A and B of G, respectively. Our main result states that G has at least fA + fB vertices for which dG (v) = f(v) holds.


Unique f-factorBipartite graphsExtremal graphs

Mathematics Subject Classificiation

Primary 05C70Secondary 05C35

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Watson Wyatt Deutschland GmbHMunichGermany
  2. 2.Lehrstuhl II für MathematikRWTH-AachenAachenGermany