Work

Sparse cycle bases for graphs with bounded genus

Year: 2026

Type: article

Abstract: The basis number of a graph G is the smallest integer k such that G admits a basis B for its cycle space, where each edge of G belongs to at most k members of B . In this note, we show that every non-planar graph that can be embedded on a surface with Euler characteristic 0 has a basis number of exactly 3, proving a conjecture of Schmeichel from 1981. Additionally, we show that any graph embeddable on a surface Σ (whether orientable or non-orientable) of genus g has a basis number of O ( log ( g ) 2 ) .

Source: European Journal of Combinatorics

DOI: 10.1016/j.ejc.2026.104371

Authors: Florian Lehner, Babak Miraftab

Institutions: University of Auckland, Carleton University

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,560

Funders: University of Auckland, Natural Sciences and Engineering Research Council of Canada