DICHROMATIC NUMBER AND FRACTIONAL CHROMATIC NUMBER

Autor: BOJAN MOHAR, HEHUI WU

Publikováno v: Forum of Mathematics, Sigma, Vol 4 (2016)

The dichromatic number of a graph $G$ is the maximum integer $k$ such that there exists an orientation of the edges of $G$ such that for every partition of the vertices into fewer than $k$ parts, at least one of the parts must contain a directed

Externí odkaz: https://doaj.org/article/c365064a067649b282527c431ed7305c

Proper orientations and proper chromatic number

Autor: Yaobin Chen, Bojan Mohar, Hehui Wu

Publikováno v: Journal of Combinatorial Theory, Series B. 161:63-85

The proper chromatic number $\Vec{\chi}(G)$ of a graph $G$ is the minimum $k$ such that there exists an orientation of the edges of $G$ with all vertex-outdegrees at most $k$ and such that for any adjacent vertices, the outdegrees are different. Two

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8ca126b157135f627aa66c726b237a6f
https://doi.org/10.1016/j.jctb.2023.02.003

Word-representability of split graphs

Autor: Sergey Kitaev, Yangjing Long, Jun Ma, Hehui Wu

Letters $x$ and $y$ alternate in a word $w$ if after deleting in $w$ all letters but the copies of $x$ and $y$ we either obtain a word $xyxy\cdots$ (of even or odd length) or a word $yxyx\cdots$ (of even or odd length). A graph $G=(V,E)$ is word-repr

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::844d50df364fa9c7cb6c2a4c7b47a236
https://strathprints.strath.ac.uk/73875/1/Kitaev_etal_JC_2020_Word_representability_of_split_graphs.pdf

Coloring tournaments: From local to global

Autor: Tien-Nam Le, Ararat Harutyunyan, Stéphan Thomassé, Hehui Wu

Publikováno v: Journal of Combinatorial Theory, Series B
Journal of Combinatorial Theory, Series B, Elsevier, 2019, 138, pp.166-171. ⟨10.1016/j.jctb.2019.01.005⟩
Journal of Combinatorial Theory, Series B, 2019, 138, pp.166-171. ⟨10.1016/j.jctb.2019.01.005⟩

The \emph{chromatic number} of a directed graph $D$ is the minimum number of colors needed to color the vertices of $D$ such that each color class of $D$ induces an acyclic subdigraph. Thus, the chromatic number of a tournament $T$ is the minimum num

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2b291b44942ab901ae45622bbce0d739
https://doi.org/10.1016/j.jctb.2019.01.005

The extremal function for disconnected minors

Autor: Endre Csóka, Hehui Wu, Sergey Norin, Irene Lo, Liana Yepremyan

Publikováno v: Journal of Combinatorial Theory, Series B. 126:162-174

For a graph H let c ( H ) denote the supremum of | E ( G ) | / | V ( G ) | taken over all non-null graphs G not containing H as a minor. We show that c ( H ) ≤ | V ( H ) | + comp ( H ) 2 − 1 , when H is a union of cycles. This verifies a conjectu

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::8f00b577d64043e5de8c79f5b2431a13
https://doi.org/10.1016/j.jctb.2017.04.005