Graph minors. V. Excluding a planar graph
Journal of Combinatorial Theory Series B
Nonconstructive tools for proving polynomial-time decidability
Journal of the ACM (JACM)
Linear time algorithms for NP-hard problems restricted to partial k-trees
Discrete Applied Mathematics
Journal of Combinatorial Theory Series B
Graph minors: X. obstructions to tree-decomposition
Journal of Combinatorial Theory Series B
Five-coloring maps on surfaces
Journal of Combinatorial Theory Series B
List colourings of planar graphs
Discrete Mathematics
Restricted colorings of graphs
Surveys in combinatorics, 1993
Every planar graph is 5-choosable
Journal of Combinatorial Theory Series B
Quickly excluding a planar graph
Journal of Combinatorial Theory Series B
Graph minors. XIII: the disjoint paths problem
Journal of Combinatorial Theory Series B
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
Journal of Combinatorial Theory Series B - Special issue: dedicated to Professor W. T. Tutte on the occasion of his eightieth birthday
Color-critical graphs on a fixed surface
Journal of Combinatorial Theory Series B - Special issue: dedicated to Professor W. T. Tutte on the occasion of his eightieth birthday
Approximate graph coloring by semidefinite programming
Journal of the ACM (JACM)
Zero knowledge and the chromatic number
Journal of Computer and System Sciences - Eleventh annual conference on structure and complexity 1996
Proof of a conjecture of Mader, Erdös and Hajnal on topological complete subgraphs
European Journal of Combinatorics
Highly connected sets and the excluded grid theorem
Journal of Combinatorial Theory Series B
Fast algorithms for K4 immersion testing
Journal of Algorithms
Graph minors. XVI. excluding a non-planar graph
Journal of Combinatorial Theory Series B
Excluding any graph as a minor allows a low tree-width 2-coloring
Journal of Combinatorial Theory Series B
Approximation algorithms for classes of graphs excluding single-crossing graphs as minors
Journal of Computer and System Sciences
Some remarks on Hajós' conjecture
Journal of Combinatorial Theory Series B
Any 7-Chromatic Graphs Has K 7 Or K 4,4 As A Minor
Combinatorica
Graph Minors. XX. Wagner's conjecture
Journal of Combinatorial Theory Series B - Special issue dedicated to professor W. T. Tutte
Algorithmic Graph Minor Theory: Decomposition, Approximation, and Coloring
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Locally planar graphs are 5-choosable
Journal of Combinatorial Theory Series B
Approximating List-Coloring on a Fixed Surface
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
List-color-critical graphs on a fixed surface
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Additive approximation algorithms for list-coloring minor-closed class of graphs
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Linear connectivity forces large complete bipartite minors
Journal of Combinatorial Theory Series B
Hadwiger's conjecture is decidable
Proceedings of the forty-first annual ACM symposium on Theory of computing
Graph minors XXIII. Nash-Williams' immersion conjecture
Journal of Combinatorial Theory Series B
On the complexity of some colorful problems parameterized by treewidth
Information and Computation
A simpler algorithm and shorter proof for the graph minor decomposition
Proceedings of the forty-third annual ACM symposium on Theory of computing
The Erdős-Pósa property for clique minors in highly connected graphs
Journal of Combinatorial Theory Series B
Characterizing graphs of small carving-width
Discrete Applied Mathematics
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A graph G contains a subdivision of H if G contains a subgraph which is isomorphic to a graph that can be obtained from H by subdividing some edges. A graph H is immersed in a graph G if the vertices of H are mapped to (distinct) vertices of G, and the edges of H are mapped to paths joining the corresponding pairs of vertices of G, in such a way that the paths are pairwise edge-disjoint. Although the well-known Kuratowski's theorem can be stated in terms of both a subdivision and a minor, we know that the notions of a subdivision and a minor do not seem to be similar. The notions of an immersion and a minor seem to be quite similar, and structural approach concerning graph minors has been extremely successful. In fact, Robertson and Seymour extended their proof of the famous Wanger's conjecture to prove that graphs are well-quasi-ordered by the immersion relation. We give additive approximation algorithms for list-coloring within 3.5(k + 1) of the list-chromatic number for graphs without Kk as a subdivision, and within 1.5(k − 1) of the list-chromatic number for graphs without Kk as an immersion. Clearly our results give rise to additive approximation algorithms for graph-coloring of graphs without Kk as a subdivision (in fact, we shall give an additive approximation algorithm within 2.5(k + 1) of the chromatic number) and Kk as an immersion, too. These are the first results in this direction (in fact, these are the first results concerning list-coloring graphs without fixed graph as a subdivision or as an immersion, except for the known upper bound results) and extend the result by Kawarabayashi, Demaine and Hajiaghayi (SODA'09) concerning the additive approximation algorithm for list-coloring graphs without Kk as a minor. We also discuss how our results are related to the famous Hájos' conjecture and Hadwiger's conjecture. We point out that it is Unique-Game hard to obtain an O(k/log2 k)-approximation algorithm for graph-coloring of graphs with maximum degree at most k − 2 [6], and hence it is also Unique-Game hard to obtain an O(k/log2 k)-approximation algorithm for graph-coloring of graphs without a Kk-subdivision or without a Kk-immersion. Therefore it really makes sense to consider an additive approximation algorithm for graph coloring of these family of graphs (which is in contrast to a 2-approximation algorithm for graph-coloring of H-minor-free graphs [13]).