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List coloring generalizes graph coloring by requiring the color of a vertex to be selected from a list of colors specific to that vertex. One refinement of list coloring, called choosability with separation, requires that the intersection of adjacent
Externí odkaz:
http://arxiv.org/abs/1512.07847
Autor:
Berikkyzy, Zhanar, Cox, Christopher, Dairyko, Michael, Hogenson, Kirsten, Kumbhat, Mohit, Lidický, Bernard, Messerschmidt, Kacy, Moss, Kevin, Nowak, Kathleen, Palmowski, Kevin F., Stolee, Derrick
Publikováno v:
Graphs and Combinatorics 33 (2017) 751-787
All planar graphs are 4-colorable and 5-choosable, while some planar graphs are not 4-choosable. Determining which properties guarantee that a planar graph can be colored using lists of size four has received significant attention. In terms of constr
Externí odkaz:
http://arxiv.org/abs/1512.03787
Autor:
Brandt, Axel, Ferrara, Michael, Kumbhat, Mohit, Loeb, Sarah, Stolee, Derrick, Yancey, Matthew
A star $k$-coloring is a proper $k$-coloring where the union of two color classes induces a star forest. While every planar graph is 4-colorable, not every planar graph is star 4-colorable. One method to produce a star 4-coloring is to partition the
Externí odkaz:
http://arxiv.org/abs/1510.03381
Autor:
Kim, Younjin, Kumbhat, Mohit, Nagy, Zoltan Lorant, Patkos, Balazs, Pokrovskiy, Alexey, Vizer, Mate
Given a graph $G$ and a positive integer $R$ we address the following combinatorial search theoretic problem: What is the minimum number of queries of the form "does an unknown vertex $v \in V(G)$ belong to the ball of radius $r$ around $u$?" with $u
Externí odkaz:
http://arxiv.org/abs/1405.7508
A $(v,k,t)$ packing of size $b$ is a system of $b$ subsets (blocks) of a $v$-element underlying set such that each block has $k$ elements and every $t$-set is contained in at most one block. $P(v,k,t)$ stands for the maximum possible $b$. A packing i
Externí odkaz:
http://arxiv.org/abs/1303.4030
For a hypergraph G and a positive integer s, let \chi_{\ell} (G,s) be the minimum value of l such that G is L-colorable from every list L with |L(v)|=l for each v\in V(G) and |L(u)\cap L(v)|\leq s for all u, v\in e\in E(G). This parameter was studied
Externí odkaz:
http://arxiv.org/abs/1109.2969
Autor:
Brandt, Axel, Ferrara, Michael, Kumbhat, Mohit, Loeb, Sarah, Stolee, Derrick, Yancey, Matthew
Publikováno v:
In European Journal of Combinatorics October 2016 57:1-12
Autor:
Kim, Younjin, Kumbhat, Mohit, Nagy, Zoltán Lóránt, Patkós, Balázs, Pokrovskiy, Alexey, Vizer, Máté
Publikováno v:
In Discrete Applied Mathematics 1 October 2015 193:39-47
Publikováno v:
In Discrete Mathematics March 2018 341(3):600-605