Degree conditions for disjoint path covers in digraphs

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2025-01-23 DOI:10.1016/j.disc.2025.114410

Ansong Ma, Yuefang Sun

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引用次数: 0

Abstract

In this paper, we study degree conditions for three types of disjoint directed path cover problems: many-to-many k-DDPC, one-to-many k-DDPC and one-to-one k-DDPC, which are intimately connected to other famous topics in graph theory, such as Hamiltonicity and linkage.

We first get two sharp minimum semi-degree sufficient conditions for the unpaired many-to-many k-DDPC problem and a sharp Ore-type degree condition for the paired many-to-many 2-DDPC problem. We then obtain a minimum semi-degree sufficient condition for the one-to-many k-DDPC problem on a digraph with order n, and show that the bound for the minimum semi-degree is sharp when

n + k

is even and is sharp up to an additive constant 1 otherwise. Finally, we give a minimum semi-degree sufficient condition for the one-to-one k-DDPC problem on a digraph with order n, and show that the bound for the minimum semi-degree is sharp when

n + k

is odd and is sharp up to an additive constant 1 otherwise. Furthermore, these results hold even when n is (at least) a linear function of k. In addition, our results improve the existing results by reducing both of the lower bounds of the order and the minimum semi-degree condition of digraphs.

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来源期刊

Discrete Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

期刊介绍： Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.