# algorithm

## Algorithm for graph homomorphisms ★★

Author(s): Fomin; Heggernes; Kratsch

\begin{question} % Enter your conjecture in LaTeX % You may change "conjecture" to "question" or "problem" if you prefer. Is there an algorithm that decides, for input graphs $G$ and $H$, whether there exists a homomorphism from $G$ to $H$ in time $O(c^{|V(G)|+|V(H)|})$ for some constant $c$? \end{question}

Keywords: algorithm; Exponential-time algorithm; homomorphism

## Is there an algorithm to determine if a triangulated 4-manifold is combinatorially equivalent to the 4-sphere? ★★★

Author(s): Novikov

\begin{problem} Is there an algorithm which takes as input a triangulated 4-manifold, and determines whether or not this manifold is combinatorially equivalent to the 4-sphere? \end{problem}