Work

Subgraphs with a positive minimum semidegree in digraphs with large outdegree

Year: 2025

Type: article

Abstract: We prove that every n -vertex directed graph G with the minimum outdegree δ + ( G ) = d contains a subgraph H satisfying min δ + ( H ) , δ - ( H ) ≥ d ( d + 1 ) 2 n . We also show that if d = o ( n ) then this bound is asymptotically best possible.

Source: Innovations in Graph Theory

DOI: 10.5802/igt.14

Authors: Andrzej Grzesik, Vojtěch Rödl, Jan Volec

Institutions: Jagiellonian University, Emory University, Czech Technical University in Prague

Language: English

Topic: Limits and Structures in Graph Theory

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: National Science Foundation, Grantová Agentura České Republiky

Awards: Extremal and probabilistic combinatorics, Collaborative Research: Extremal and Ramsey Problems for Graphs and Hypergraphs