![](/files/happy5.png)
choosability
Choosability of Graph Powers ★★
Author(s): Noel
![$ f(k)=o(k^2) $](/files/tex/bd642e5dd66f1577cedf5fed57f75187a80168ac.png)
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![\[\text{ch}\left(G^2\right)\leq f\left(\chi\left(G^2\right)\right)?\]](/files/tex/989db06683633e86605c26e7d9f0bffc7e46a496.png)
Keywords: choosability; chromatic number; list coloring; square of a graph
Bounding the on-line choice number in terms of the choice number ★★
Author(s): Zhu
![$ \text{ch}^{\text{OL}}-\text{ch} $](/files/tex/3aa1320c57f076f184f0f05f44e350d3ffea4fa4.png)
Keywords: choosability; list coloring; on-line choosability
Choice number of complete multipartite graphs with parts of size 4 ★
Author(s):
![$ K_{4*k} $](/files/tex/82ec98d99adaa09f09a47abdba94f938b9872a70.png)
![$ k $](/files/tex/c450c3185f7285cfa0b88d3a903c54f7df601201.png)
Keywords: choosability; complete multipartite graph; list coloring
Choice Number of k-Chromatic Graphs of Bounded Order ★★
Author(s): Noel
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ k $](/files/tex/c450c3185f7285cfa0b88d3a903c54f7df601201.png)
![$ mk $](/files/tex/c6307bea3dbafaf140155114bd35bb788fc000d8.png)
![$ \text{ch}(G)\leq \text{ch}(K_{m*k}) $](/files/tex/0d0a9568608331000410c601a041b1c391b31d01.png)
Keywords: choosability; complete multipartite graph; list coloring
Circular choosability of planar graphs ★
Author(s): Mohar
Let be a graph. If
and
are two integers, a
-colouring of
is a function
from
to
such that
for each edge
. Given a list assignment
of
, i.e.~a mapping that assigns to every vertex
a set of non-negative integers, an
-colouring of
is a mapping
such that
for every
. A list assignment
is a
-
-list-assignment if
and
for each vertex
. Given such a list assignment
, the graph G is
-
-colourable if there exists a
-
-colouring
, i.e.
is both a
-colouring and an
-colouring. For any real number
, the graph
is
-
-choosable if it is
-
-colourable for every
-
-list-assignment
. Last,
is circularly
-choosable if it is
-
-choosable for any
,
. The circular choosability (or circular list chromatic number or circular choice number) of G is
Keywords: choosability; circular colouring; planar graphs
Ohba's Conjecture ★★
Author(s): Ohba
![$ |V(G)|\leq 2\chi(G)+1 $](/files/tex/4a7472498fbaf9edea55531f6e3927a3336b2285.png)
![$ \chi_\ell(G)=\chi(G) $](/files/tex/0a2573f7d1a57016f919f018635cd3f9f9875fc4.png)
Keywords: choosability; chromatic number; complete multipartite graph; list coloring
![Syndicate content Syndicate content](/misc/feed.png)