cubic graph

3-Decomposition Conjecture ★★★

Author(s): Arthur; Hoffmann-Ostenhof

\begin{conjecture} (3-Decomposition Conjecture) Every connected cubic graph $G$ has a decomposition into a spanning tree, a family of cycles and a matching. \end{conjecture}

Keywords: cubic graph

Domination in cubic graphs ★★

Author(s): Reed

\begin{problem} Does every 3-connected cubic graph $G$ satisfy $\gamma(G) \le \lceil |G|/3 \rceil$ ? \end{problem}

Keywords: cubic graph; domination

Universal Steiner triple systems ★★

Author(s): Grannell; Griggs; Knor; Skoviera

\begin{problem} Which \href [Steiner triple systems]{} are universal? \end{problem}

Keywords: cubic graph; Steiner triple system

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