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- W2013289164 abstract "One way to state the Load Coloring Problem (LCP) is as follows. Let $G=(V,E)$ be graph and let $f:Vrightarrow {{rm red}, {rm blue}}$ be a 2-coloring. An edge $ein E$ is called red (blue) if both end-vertices of $e$ are red (blue). For a 2-coloring $f$, let $r'_f$ and $b'_f$ be the number of red and blue edges and let $mu_f(G)=min{r'_f,b'_f}$. Let $mu(G)$ be the maximum of $mu_f(G)$ over all 2-colorings. We introduce the parameterized problem $k$-LCP of deciding whether $mu(G)ge k$, where $k$ is the parameter. We prove that this problem admits a kernel with at most $7k$. Ahuja et al. (2007) proved that one can find an optimal 2-coloring on trees in polynomial time. We generalize this by showing that an optimal 2-coloring on graphs with tree decomposition of width $t$ can be found in time $O^*(2^t)$. We also show that either $G$ is a Yes-instance of $k$-LCP or the treewidth of $G$ is at most $2k$. Thus, $k$-LCP can be solved in time $O^*(4^k).$" @default.
- W2013289164 created "2016-06-24" @default.
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- W2013289164 date "2013-08-08" @default.
- W2013289164 modified "2023-09-27" @default.
- W2013289164 title "Parameterized Algorithms for Load Coloring Problem" @default.
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