2017/12/05 by Nanao Kita, Kita, Nanao · 1 citation
Computer Science · Engineering · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1712.01920
openalex publication_date 2017/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper is the first from a series of papers that establish a generalization of the basilica decomposition for cardinality minimum joins in grafts. Joins in grafts are also known as T-joins in graphs, where T is a given set of vertices, and minimum joins in grafts can be considered as a generalization of perfect matchings in graphs provided in terms of parity. The basilica decomposition is a canonical decomposition applicable to general graphs with perfect matchings, and the general Kotzig-Lovász decomposition is one of the three central concepts that compose this theory. The classical Kotzig-Lovász decomposition is a canonical decomposition for a special class of graphs known as \em factor-connected graphs and is famous for its contribution to the study of the matching polytope and lattice. The general Kotzig-Lovász decomposition is a nontrivial generalization of its classical counterpart and is applicable to general graphs with perfect matchings. As a component of the basilica decomposition theory, the general Kotzig-Lovász decomposition has contributed to the derivation of further results in matching theory, such as a characterization of barriers or an alternative proof of the tight cut lemma. In this paper, we present an analogue of the general Kotzig-Lovász decomposition for minimum joins in grafts.