
Complexity of the list homomorphism problem in hereditary graph classes
A homomorphism from a graph G to a graph H is an edgepreserving mapping...
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Complexity of C_kcoloring in hereditary classes of graphs
For a graph F, a graph G is Ffree if it does not contain an induced sub...
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Choosability in bounded sequential list coloring
The list coloring problem is a variation of the classical vertex colorin...
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The polynomial method for listcolouring extendability of outerplanar graphs
We restate theorems of Hutchinson on listcolouring extendability for ou...
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Coloring Problems on Bipartite Graphs of Small Diameter
We investigate a number of coloring problems restricted to bipartite gra...
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Digraphs Homomorphism Problems with Maltsev Condition
We consider a generalization of finding a homomorphism from an input dig...
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Efficiently listedge coloring multigraphs asymptotically optimally
We give polynomial time algorithms for the seminal results of Kahn, who ...
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Sparsification Lower Bounds for List HColoring
We investigate the List HColoring problem, the generalization of graph coloring that asks whether an input graph G admits a homomorphism to the undirected graph H (possibly with loops), such that each vertex v ∈ V(G) is mapped to a vertex on its list L(v) ⊆ V(H). An important result by Feder, Hell, and Huang [JGT 2003] states that List HColoring is polynomialtime solvable if H is a socalled biarc graph, and NPcomplete otherwise. We investigate the NPcomplete cases of the problem from the perspective of polynomialtime sparsification: can an nvertex instance be efficiently reduced to an equivalent instance of bitsize O(n^2ε) for some ε > 0? We prove that if H is not a biarc graph, then List HColoring does not admit such a sparsification algorithm unless NP ⊆ coNP/poly. Our proofs combine techniques from kernelization lower bounds with a study of the structure of graphs H which are not biarc graphs.
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