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list coloring
List Colourings of Complete Multipartite Graphs with 2 Big Parts ★★
Author(s): Allagan
![$ 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) $](/files/tex/bd7ca9e1076d95097ac657d98e06895400a68ec0.png)
Keywords: complete bipartite graph; complete multipartite graph; list coloring
List Total Colouring Conjecture ★★
Author(s): Borodin; Kostochka; Woodall
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ \chi_\ell(G)=\chi(G) $](/files/tex/0a2573f7d1a57016f919f018635cd3f9f9875fc4.png)
Keywords: list coloring; Total coloring; total graphs
Choosability of Graph Powers ★★
Author(s): Noel
![$ 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}) $](/files/tex/0d0a9568608331000410c601a041b1c391b31d01.png)
Keywords: choosability; complete multipartite graph; list coloring
Ohba's Conjecture ★★
Author(s): Ohba
![$ |V(G)|\leq 2\chi(G)+1 $](/files/tex/4a7472498fbaf9edea55531f6e3927a3336b2285.png)
![$ \chi_\ell(G)=\chi(G) $](/files/tex/0a2573f7d1a57016f919f018635cd3f9f9875fc4.png)
Keywords: choosability; chromatic number; complete multipartite graph; list coloring
Partial List Coloring ★★★
Author(s): Iradmusa
Let be a simple graph, and for every list assignment
let
be the maximum number of vertices of
which are colorable with respect to
. Define
, where the minimum is taken over all list assignments
with
for all
.
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ \chi_\ell $](/files/tex/46e2d5b6cf87b7e24d9ac72345043107b7ccae3a.png)
![$ 1\leq r\leq s\leq \chi_\ell $](/files/tex/a3fc6cd4c98fabb35869474a493492a0435792e7.png)
![\[\frac{\lambda_r}{r}\geq\frac{\lambda_s}{s}.\]](/files/tex/47be18e956355dd433b88b66eabf01a9e3ed5f61.png)
Keywords: list assignment; list coloring
Partial List Coloring ★★★
Author(s): Albertson; Grossman; Haas
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ n $](/files/tex/ec63d7020a64c039d5f6703b8fa3ab7393358b5b.png)
![$ \chi_\ell(G) $](/files/tex/b68082745a25a09294e2c92c006b61d3ef1a9e54.png)
![$ 0\leq t\leq \chi_\ell $](/files/tex/1aee119babfe25de435c7cf6beff3114a5ae9326.png)
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ t $](/files/tex/4761b031c89840e8cd2cda5b53fbc90c308530f3.png)
![$ \frac{tn}{\chi_\ell(G)} $](/files/tex/59b72b19d6799e1fd7a0fc093bff9283068dc838.png)
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
Keywords: list assignment; list coloring
List colorings of edge-critical graphs ★★
Author(s): Mohar
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ \Delta $](/files/tex/e3f8e135c571143e94f1d4f236326b862080b200.png)
![$ e $](/files/tex/5105762e0c97083905ebf07919c7d4d5ed38dce3.png)
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ L(e) $](/files/tex/bd0dfc00a21966b9e90231c00dab0d0aa81a0ab0.png)
![$ \Delta $](/files/tex/e3f8e135c571143e94f1d4f236326b862080b200.png)
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ L $](/files/tex/73f33398d7e8aa42e6ec25ee2bb4f2b57ed3391a.png)
Keywords: edge-coloring; list coloring
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