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GH from MO
GH from MO
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added constraint to rule out self loops and multiple edges and corrected the degree constraint
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Manfred Weis
Manfred Weis
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Question:

what can be said about the existence of $2k+1$$2k$ regular graphs, $0\lt k$$1\lt k$ that have a $1$-factor and a $2$-factor?

Provided their existence, what is/are the smallest for $k$?

The graphs must be simple, i.e. they must not neither have self-loops nor multiple edges.

Question:

what can be said about the existence of $2k+1$ regular graphs, $0\lt k$ that have a $1$-factor and a $2$-factor?

Provided their existence, what is/are the smallest for $k$?

Question:

what can be said about the existence of $2k$ regular graphs, $1\lt k$ that have a $1$-factor and a $2$-factor?

Provided their existence, what is/are the smallest for $k$?

The graphs must be simple, i.e. they must not neither have self-loops nor multiple edges.

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Manfred Weis
Manfred Weis
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Existence of certain regular graphs

Question:

what can be said about the existence of $2k+1$ regular graphs, $0\lt k$ that have a $1$-factor and a $2$-factor?

Provided their existence, what is/are the smallest for $k$?