论文信息 - Note on non-separating and removable cycles in highly connected graphs

Note on non-separating and removable cycles in highly connected graphs

We combine two well-known results by Mader and Thomassen, respectively. Namely, we prove that for any k-connected graph G (k>=4), there is an induced cycle C such that G-V(C) is (k-3)-connected and G-E(C) is (k-2)-connected. Both ''(k-3)-connected'' and ''(k-2)-connected'' are best possible in a sense.

Ken-ichi Kawarabayashi | Shinya Fujita

[1] Ken-ichi Kawarabayashi,et al. Contractible Edges and Triangles in k-Connected Graphs , 2002, J. Comb. Theory, Ser. B.

[2] Yoshimi Egawa,et al. Contractible edges in non-separating cycles , 1991, Comb..

[3] Carsten Thomassen,et al. Nonseparating cycles in K-Connected graphs , 1981, J. Graph Theory.

[4] Yoshimi Egawa. Contractible Cycles in Graphs with Girth at Least 5 , 1998, J. Comb. Theory, Ser. B.

[5] Bill Jackson. Removable Cycles in 2‐Connected Graphs of Minimum Degree at Least Four , 1980 .

[6] Bruce A. Reed,et al. A weaker version of Lovász' path removal conjecture , 2008, J. Comb. Theory, Ser. B.

[7] Yoshimi Egawa,et al. Cycles in k-connected graphs whose deletion results in a (k-2)-connected graph , 1987, J. Comb. Theory, Ser. B.

[8] Sean McGuinness. Contractible bonds in graphs , 2005, J. Comb. Theory, Ser. B.

[9] Jan van den Heuvel,et al. Removable Circuits in Multigraphs , 1997, J. Comb. Theory, Ser. B.

[10] W. Mader,et al. kreuzungsfreiea,b-Wege in endlichen Graphen , 1974 .

[11] MATTHIAS KRIESELL. Triangle Density and Contractibility , 2005, Comb. Probab. Comput..