Abstract
The subgraph of a 5-connected graph G induced by the set of degree 5 vertices is said to be the 5-subgraph of G. An edge of a 5-connected graph is said to be 5-contractible if the contraction of the edge results in a 5-connected graph. A 5-connected graph with no 5-contractible edge is said to be contraction-critically 5-connected. We show that there are exact two graphs with order 5 which can be a component of the 5-subgraph of a contraction-critically 5-connected graph.
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Ando, K. Small Components of the 5-Subgraph of a Contraction-critically 5-Connected Graph. Graphs and Combinatorics 33, 1485–1497 (2017). https://doi.org/10.1007/s00373-017-1830-3
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DOI: https://doi.org/10.1007/s00373-017-1830-3