P. Francis

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math.CO2024

Maximal Independent Sets in Planar Triangulations

P. Francis, Abraham M. Illickan, Lijo M. Jose +1

We show that every planar triangulation on $n$ vertices has a maximal independent set of size at most $n /3$ . This affirms a conjecture by Botler, Fernandes and Gutiérrez [Electron.…

math.CO2024

Face-hitting Dominating Sets in Planar Graphs

P. Francis, Abraham M. Illickan, Lijo M. Jose +1

A dominating set of a graph $G$ is a subset $S$ of its vertices such that each vertex of $G$ not in $S$ has a neighbor in $S$ . A face-hitting set of a plane graph $G$ is a set $T$ …