The Cheeger Cut and Cheeger Problem in Metric Graphs

2022/03/15 by José M. Mazón, Mazón, José M. · 2 citations
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2203.07760

openalex publication_date 2022/03/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For discrete weighted graphs there is sufficient literature about the Cheeger cut and the Cheeger problem, but for metric graphs there are few results about these problems. Our aim is to study the Cheeger cut and the Cheeger problem in metric graphs. For that, we use the concept of total variation and perimeter in metric graphs introduced in \citeMazon, which takes into account the jumps at the vertices of the functions of bounded variation. Moreover, we study the eigenvalue problem for the minus 1-Laplacian operator in metric graphs, whereby we give a method to solve the optimal Cheeger cut problem.

Cited by

• Combinatorial Courant-Fischer-Weyl Minimax Principle on Cheeger k-constants of Weighted Forests
• Eigenvalues of the discrete p-Laplacian via graph surgery

Related

• Cheeger inequalities for unbounded graph Laplacians
• The Total Variation Flow in Metric Graphs
• Optimal Cheeger cuts and bisections of random geometric graphs
• Gaps between consecutive eigenvalues for compact metric graphs
• On the Cheeger constant for distance-regular graphs