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edit approved Dec 2, 2023 at 10:21
The Amplitwist
edit approved Dec 2, 2023 at 10:21
The Amplitwist
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The Erdős–Gallai theoremErdős–Gallai theorem characterizes which degree sequences are graphical (i.e. realizable by a simple graph).

There has been some work on which degree sequences are planar graphical (i.e. realizable by a simple planar graph). See, for example, On Planar Graphical Degree Sequences by Schmeichel and HakimiOn Planar Graphical Degree Sequences by Schmeichel and Hakimi (1977).

What is currently known about which degree sequences are planar graphical?

The Erdős–Gallai theorem characterizes which degree sequences are graphical (i.e. realizable by a simple graph).

There has been some work on which degree sequences are planar graphical (i.e. realizable by a simple planar graph). See, for example, On Planar Graphical Degree Sequences by Schmeichel and Hakimi (1977).

What is currently known about which degree sequences are planar graphical?

The Erdős–Gallai theorem characterizes which degree sequences are graphical (i.e. realizable by a simple graph).

There has been some work on which degree sequences are planar graphical (i.e. realizable by a simple planar graph). See, for example, On Planar Graphical Degree Sequences by Schmeichel and Hakimi (1977).

What is currently known about which degree sequences are planar graphical?

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Tyson Williams
Tyson Williams
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Which degree sequences are planar graphical?

The Erdős–Gallai theorem characterizes which degree sequences are graphical (i.e. realizable by a simple graph).

There has been some work on which degree sequences are planar graphical (i.e. realizable by a simple planar graph). See, for example, On Planar Graphical Degree Sequences by Schmeichel and Hakimi (1977).

What is currently known about which degree sequences are planar graphical?