论文信息 - Contractile Triples in 3-Connected Graphs

Contractile Triples in 3-Connected Graphs

We prove that every 3-connected graph G of order at least nine has two adjacent edges xy and yz such that the graph obtained from G by contracting x, y, and z into a single vertex is also 3-connected.

Katsuhiro Ota | William McCuaig | K. Ota | W. McCuaig

[1] William T. Tutte,et al. A theory of 3-connected graphs , 1961 .

[2] Hikoe Enomoto,et al. Contractible edges in 3-connected graphs , 1987, J. Comb. Theory, Ser. B.

[3] R. Halin. Zur Theorie dern-fach zusammenhängenden Graphen , 1969 .

[4] L. Lovász. A homology theory for spanning tress of a graph , 1977 .

[5] Katsuhiro Ota. The number of contractible edges in 3-connected graphs , 1988, Graphs Comb..