A constant-factor approximation for weighted bond cover ☆

The WEIGHTED F-VERTEX DELETION for a class F of graphs asks, weighted graph G, for a minimum weight vertex set S such that G - S is an element of F. The case when F is minor-closed and excludes some graph as a minor has received particular attention but a constantfactor approximation remained elusive for WEIGHTED F-VERTEX DELETION. Only three cases of minor-closed Fare known to admit constant-factor approximations, namely VERTEX COVER, FEEDBACK VERTEX SET and DIAMOND HITTING SET. We study the problem for the class F of Bc-minor-free graphs, under the equivalent setting of the WEIGHTED c-BOND COVER problem, and present a constant-factor approximation algorithm using the primal-dual method. Besides making an important step in the quest of (dis)proving a constant-factor approximation for WEIGHTED F-VERTEX DELETION, our result may be useful as a template for algorithms for other minor-closed families. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.