Planar Digraphs without Large Acyclic Sets | Zendy

Knauer Kolja | Zendy; Valicov Petru | Zendy; Wenger Paul S. | Zendy

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Planar Digraphs without Large Acyclic Sets

Author(s) -

Knauer Kolja,

Valicov Petru,

Wenger Paul S.

Publication year - 2017

Publication title -

journal of graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.164

H-Index - 54

eISSN - 1097-0118

pISSN - 0364-9024

DOI - 10.1002/jgt.22061

Subject(s) - directed acyclic graph , combinatorics , feedback arc set , mathematics , directed graph , conjecture , planar graph , set (abstract data type) , discrete mathematics , graph , planar , computer science , line graph , computer graphics (images) , voltage graph , programming language

Given a directed graph, an acyclic set is a set of vertices inducing a directed subgraph with no directed cycle. In this note, we show that for all integers n ≥ g ≥ 3 , there exist oriented planar graphs of order n and digirth g for which the size of the maximum acyclic set is at most ⌈ n ( g − 2 ) + 1 g − 1 ⌉ . When g = 3 this result disproves a conjecture of Harutyunyan and shows that a question of Albertson is best possible.

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