Geodesic
Chordal directed graphs are not \(\chi\)-bounded
The electronic journal of combinatorics, Tome 29 (2022) no. 2
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We show that digraphs with no transitive tournament on $3$ vertices and in which every induced directed cycle has length $3$ can have arbitrarily large dichromatic number. This answers in the negative a question of Carbonero, Hompe, Moore, and Spirkl (and strengthens one of their results).
DOI : 10.37236/11050
Classification : 05C20, 05C15, 05C38, 05C12, 05C70, 05C75
Mots-clés : dicoloring, dichromatic number, chordal digraph 
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     author = {Pierre Aboulker and Nicolas Bousquet and R\'emi de Verclos},
     title = {Chordal directed graphs are not \(\chi\)-bounded},
     journal = {The electronic journal of combinatorics},
     year = {2022},
     volume = {29},
     number = {2},
     doi = {10.37236/11050},
     zbl = {1493.05130},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/11050/}
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Pierre Aboulker; Nicolas Bousquet; Rémi de Verclos. Chordal directed graphs are not \(\chi\)-bounded. The electronic journal of combinatorics, Tome 29 (2022) no. 2. doi: 10.37236/11050

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