Abstract
We present heuristics and algorithms with polynomial expected running time for coloring semirandom k-colorable graphs made up as follows. Partition the vertex set V={1,...,n} into k classes V 1,...,V k randomly and include each V i -V j -edge \((i\not=j)\) with probability p independently. Then, an adversary adds further V i -V j -edges \((i\not=j)\). We show that if np ≥ max {(1 + ε)kln (n),Ck 2}, an optimal coloring can be found in polynomial time with high probability. Furthermore, if np ≥ C max {kln (n),k 2ln (k)}, an optimal coloring can be found in polynomial expected time. By contrast, it is NP-hard to find a k-coloring whp. if \(np\leq(\frac12-\varepsilon)k\ln(n/k)\).
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Coja-Oghlan, A. (2004). Coloring Semirandom Graphs Optimally. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds) Automata, Languages and Programming. ICALP 2004. Lecture Notes in Computer Science, vol 3142. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27836-8_34
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DOI: https://doi.org/10.1007/978-3-540-27836-8_34
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