R. Thomas. Recent excluded minor theorems. A survey for the British Combinatorial Conference.  Home/Search   Document Details and Download   Summary   Related Articles

....in the projective plane and Archdeacon [1] showed that there are 35 minor minimal graphs not embeddable in the projective plane. The lists of such excluded graphs for all other surfaces are not known, and evidence indicates that they might contain too many graphs to be of any practical use [20]. Archdeacon and Huneke [2] then showed that for any non orientable surface S there exists a finite family of graphs F S such that a graph G is embeddable in S if and only if G has no minor isomorphic to a member of F S . The members of F S are called the excluded minors of embeddability in S. In ....

....has a Hamiltonian cycle) or not k colorable (respectively has no Hamiltonian cycle) for each fixed w and k. 6 Wagner s conjecture In this section we describe Robertson and Seymour s proof of Wagner s conjecture [15] The material presented here is based largely upon a survey by Thomas [20], because Robertson and Seymour s paper [15] has not been published yet . The proof is similar to theorem 5.5 and corollary 5.6. Given a graph G let G Gamma G = fG : G is not a minor of G g. Take a sequence of graphs (G i ) i=1 . If there is an i 1 such that G 1 m G i we are done. ....

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R. Thomas. Recent excluded minor theorems. A survey for the British Combinatorial Conference.

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