
The intersection of two vertex coloring problems
A hole is an induced cycle with at least four vertices. A hole is even i...
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Note on 3Coloring of (2P_4,C_5)Free Graphs
We show that the 3coloring problem is polynomialtime solvable on (2P_4...
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Sparsification Lower Bounds for List HColoring
We investigate the List HColoring problem, the generalization of graph ...
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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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Fourcoloring P_6free graphs. I. Extending an excellent precoloring
This is the first paper in a series whose goal is to give a polynomial t...
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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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Connected greedy coloring Hfree graphs
A connected ordering (v_1, v_2, ..., v_n) of V(G) is an ordering of the ...
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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 subgraph isomorphic to F. For two graphs G and H, an Hcoloring of G is a mapping f:V(G)→ V(H) such that for every edge uv∈ E(G) it holds that f(u)f(v)∈ E(H). We are interested in the complexity of the problem H Coloring, which asks for the existence of an Hcoloring of an input graph G. In particular, we consider H Coloring of Ffree graphs, where F is a fixed graph and H is an odd cycle of length at least 5. This problem is closely related to the well known open problem of determining the complexity of 3 Coloring of P_tfree graphs. We show that for every odd k ≥ 5 the C_k Coloring problem, even in the list variant, can be solved in polynomial time in P_9free graphs. The algorithm extends for the case of list version of C_k Coloring, where k is an even number of length at least 10. On the other hand, we prove that if some component of F is not a subgraph of a subdividecd claw, then the following problems are NPcomplete in Ffree graphs: a)extension version of C_k Coloring for every odd k ≥ 5, b) list version of C_k Coloring for every even k ≥ 6.
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