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Wiederrecht, Sebastian
이산수학 그룹
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Colouring non-even digraphs

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Title
Colouring non-even digraphs
Author(s)
Millani, Marcelo Garlet; Steiner, Raphael; Sebastian Wiederrecht
Publication Date
2022-10
Journal
Electronic Journal of Combinatorics, v.29, no.4
Publisher
Australian National University
Abstract
© The authors. Released under the CC BY-ND license (International 4.0).A colouring of a digraph as defined by Neumann-Lara in 1982 is a vertex-colouring such that no monochromatic directed cycles exist. The minimal number of colours required for such a colouring of a loopless digraph is defined to be its dichromatic number. This quantity has been widely studied in the last decades and can be considered as a natural directed analogue of the chromatic number of a graph. A digraph D is called even if for every 0-1-weighting of the edges it contains a directed cycle of even total weight. We show that every non-even digraph has dichromatic number at most 2 and an optimal colouring can be found in polynomial time. We strengthen a previously known NP-hardness result by showing that deciding whether a directed graph is 2-colourable remains NP-hard even if it contains a feedback vertex set of bounded size.
URI
https://pr.ibs.re.kr/handle/8788114/12696
DOI
10.37236/8800
ISSN
1077-8926
Appears in Collections:
Pioneer Research Center for Mathematical and Computational Sciences(수리 및 계산과학 연구단) > Discrete Mathematics Group(이산 수학 그룹) > 1. Journal Papers (저널논문)
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