Contractible edges in 3-connected graphs (Q1087557)
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scientific article; zbMATH DE number 3987315
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Contractible edges in 3-connected graphs |
scientific article; zbMATH DE number 3987315 |
Statements
Contractible edges in 3-connected graphs (English)
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1987
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An edge whose contraction results in a 3-connected graph is called a contractible edge. Using two theorems of \textit{R. Halin} [Math. Ann. 182, 175-188 (1969; Zbl 0175.505); Abh. Sem. Univ. Hamburg 33, 133-163 (1969; Zbl 0175.505)] it is easy to see that every 3-connected graph G of order least five has \(\lceil (| G| +3)/5\rceil\) or more contractible edges. The authors improved this bound to \(\lceil | G| /2\rceil\) and characterizes those 3-connected graphs which attain the equality.
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contractible edges
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