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complete multipartite graph
List Colourings of Complete Multipartite Graphs with 2 Big Parts ★★
Author(s): Allagan
Question Given
, what is the smallest integer
such that
?
![$ a,b\geq2 $](/files/tex/7ae98b0c55d36dcaf7def20925869c5d4b1d48ef.png)
![$ t\geq0 $](/files/tex/13168e3697d72526aed2db7c8042d868fd46bc7e.png)
![$ \chi_\ell(K_{a,b}+K_t)= \chi(K_{a,b}+K_t) $](/files/tex/bd7ca9e1076d95097ac657d98e06895400a68ec0.png)
Keywords: complete bipartite graph; complete multipartite graph; list coloring
Choice number of complete multipartite graphs with parts of size 4 ★
Author(s):
Question What is the choice number of
for general
?
![$ K_{4*k} $](/files/tex/82ec98d99adaa09f09a47abdba94f938b9872a70.png)
![$ k $](/files/tex/c450c3185f7285cfa0b88d3a903c54f7df601201.png)
Keywords: choosability; complete multipartite graph; list coloring
Choice Number of k-Chromatic Graphs of Bounded Order ★★
Author(s): Noel
Conjecture If
is a
-chromatic graph on at most
vertices, then
.
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ k $](/files/tex/c450c3185f7285cfa0b88d3a903c54f7df601201.png)
![$ mk $](/files/tex/c6307bea3dbafaf140155114bd35bb788fc000d8.png)
![$ \text{ch}(G)\leq \text{ch}(K_{m*k}) $](/files/tex/0d0a9568608331000410c601a041b1c391b31d01.png)
Keywords: choosability; complete multipartite graph; list coloring
Ohba's Conjecture ★★
Author(s): Ohba
Conjecture If
, then
.
![$ |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
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