On the Packing Partitioning Problem on Directed Graphs

Babak Samadi and Ismael G. Yero
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Babak Samadi: Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran 1993893973, Iran
Ismael G. Yero: Departamento de Matemáticas, Universidad de Cádiz, 11202 Algeciras, Spain

Mathematics, 2021, vol. 9, issue 23, 1-12

Abstract: This work is aimed to continue studying the packing sets of digraphs via the perspective of partitioning the vertex set of a digraph into packing sets (which can be interpreted as a type of vertex coloring of digraphs) and focused on finding the minimum cardinality among all packing partitions for a given digraph D , called the packing partition number of D . Some lower and upper bounds on this parameter are proven, and their exact values for directed trees are given in this paper. In the case of directed trees, the proof results in a polynomial-time algorithm for finding a packing partition of minimum cardinality. We also consider this parameter in digraph products. In particular, a complete solution to this case is presented when dealing with the rooted products.

Keywords: packing number; packing partition number; Cartesian product; direct product; lexicographic product; strong product; rooted product; directed tree (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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