Count matroids of group-labeled graphs

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Abstract

A graph G = (V, E) is called (k, ℓ)-sparse if |F| ≤ k|V (F)| − ℓ for any nonempty FE, where V (F) denotes the set of vertices incident to F. It is known that the family of the edge sets of (k, ℓ)-sparse subgraphs forms the family of independent sets of a matroid, called the (k, ℓ)-count matroid of G. In this paper we shall investigate lifts of the (k, ℓ)- count matroids by using group labelings on the edge set. By introducing a new notion called near-balancedness, we shall identify a new class of matroids whose independence condition is described as a count condition of the form |F| ≤ k|V (F)|−ℓ+αψ (F) for some function αψ determined by a given group labeling ψ on E.

Mathematics Subject Classification (2000)

05B35 52C25 

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Copyright information

© János Bolyai Mathematical Society and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Research Institute for Mathematical SciencesKyoto UniversitySakyo-ku, KyotoJapan
  2. 2.Centrum Wiskunde & Informatica (CWI)AmsterdamThe Netherlands

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