We prove that an internally 4-connected binary matroid with no minor isomorphic to MÃ°K3;3Ãž;M Ã°K3;3Ãž;MÃ°K5Ãž; or M Ã°K5Ãž is either planar or isomorphic to F7 or F 7 : As a corollary, we prove an extremalâ€¦ (More)

We prove that, if M is a weakly 4-connected matroid with |E(M)| â‰¥ 7 and neither M nor M is isomorphic to the cycle matroid of a ladder, then M has a proper minor M â€² such that M â€² is weaklyâ€¦ (More)

We prove that if N is an internally 4-connected minor of an internally 4-connected binary matroid M with E(N) â‰¥ 4, then there exist matroids M0,M1, . . . ,Mn such that M0 âˆ¼= N , Mn = M , and, forâ€¦ (More)

Graph labelings related with communication networks have been extensively investigated because their applications to real problems. Some results on graph labellings are obtained here. Scale-freeâ€¦ (More)

2010 3rd International Conference on Biomedicalâ€¦

2010

Bang-Jensen and Gutin considered the Bennett's model of chromosome arrangement in a cell of an eukaryotic organism. By means of the graph-theoretic model obtained by graph labellings, mathematiciansâ€¦ (More)