Abstract: For a fixed "pattern" graph $G$, the $\textit{colored $G$-subgraph isomorphism problem}$ (denoted $\mathrm{SUB}(G)$) asks, given an $n$-vertex graph $H$ and a coloring $V(H) \to V(G)$, whether $H$ contains a properly colored copy of $G$. The complexity of this problem is tied to parameterized versions of $\mathit{P}$ ${=}?$ $\mathit{NP}$ and $\mathit{L}$ ${=}?$ $\mathit{NL}$, among other questions. An overarching goal is to understand the complexity of $\mathrm{SUB}(G)$, under different computational models, in terms of natural invariants of th...
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Topics: 
Combinatorics
Discrete mathematics