Case 6 of hadwiger's conjecture. III. The problem of 7-vertices
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The neighbourhoodsubgraph of the 7- vertices, which is the subgraph induced by the neighbour vertices of a vertex of degree 7, is investigated; they present 124 different types.About:
This article is published in Discrete Mathematics.The article was published on 1993-02-22 and is currently open access. It has received 3 citations till now. The article focuses on the topics: Neighbourhood (graph theory) & Graph homomorphism.read more
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On The Hadwiger's Conjecture
TL;DR: In this article, the Hadwiger's conjecture was shown to be equivalent to the original Theorem which is equivalent to Theorem 1 in this paper, which is known as Theorem 2.
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A simple dissertation around the Berge problem and the Hadwiger conjecture
TL;DR: In this paper, it was shown that the Hadwiger conjecture is equivalent to a very small class of analytic conjecture stated on a small set of graphs, which is the case of the Berge problem.
Journal Article
The Analytic Reformulation of the Hadwiger Conjecture
TL;DR: In this article, it was shown that to solve the Hadwiger conjecture is equivalent to solving an analytic conjecture stated on a very small class of graphs, i.e., the maximum number of vertices of a graph that is contractible to the complete graph.
References
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Graph minors. IX. Disjoint crossed paths
TL;DR: It is shown that either modulo (≤3)-separations, G can be drawn in a disc with no crossings except in one “small” area, and with its special vertices on the outside in the correct order.
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Hadwiger's conjecture (:0U k = 6): neighbour configurations of 6-vertices in contraction-critical graphs
TL;DR: To contract a graph G consists in deleting the vertices and edges of a connected subgraph H of G, which is replaced with a new vertex h; the edges of G having one end in H are replaced with edges joining G–H with h, the other end remaining unchanged; multiple edges or loops occasionally resulting from this operation are eliminated.
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Hadwiger's conjecture: k =6. II—reductions of 6 degree vertex in 6-chromatic contraction-critical graphs
TL;DR: In this paper, a sous-graphe de voisinage d'un sommet de degre 6 contient deux triangles without sommets commun (types A, B, C, D, E, F) or constitue d'une roue W6 (type J) or d'one roue w6 privee deux rayons consecutifs (type G), on obtient ici la reduction du type J; on montre que le type G est incompatible avec les autres types.