Dirac's conjecture on K5-subdivisions
نویسندگان
چکیده
منابع مشابه
Embedding Graphs Containing K5-Subdivisions
Given a non-planar graph G with a subdivision of K5 as a subgraph, we can either transform the K5-subdivision into a K3,3-subdivision if it is possible, or else we obtain a partition of the vertices of G\K5 into equivalence classes. As a result, we can reduce a projective planarity or toroidality algorithm to a small constant number of simple planarity checks [6] or to a K3,3-subdivision in the...
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A well known theorem of Kuratowski states that a graph is planar iff it contains no subdivision of K5 or K3,3. Seymour conjectured in 1977 that every 5-connected nonplanar graph contains a subdivision of K5. In this paper, we prove several results about independent paths (no vertex of a path is internal to another), which are then used to prove Seymour’s conjecture for two classes of graphs. Th...
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Seymour and, independently, Kelmans conjectured in the 1970s that every 5-connected nonplanar graph contains a subdivision of K5. In this paper, we prove this conjecture for graphs containing K− 4 . AMS Subject Classification: 05C
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We prove the thrackle conjecture for K5 and K3,3. To do this we reduce the problem to a set of simultaneous quadratic equations over Z2. Parts of this proof are computer assisted.
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For a simplicial complex ∆ we study the effect of barycentric subdivision on ring theoretic invariants of its StanleyReisner ring. In particular, for Stanley-Reisner rings of barycentric subdivisions we verify a conjecture by Huneke and Herzog & Srinivasan, that relates the multiplicity of a standard graded k-algebra to the product of the maximal shifts in its minimal free resolution up to the ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1997
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(96)00206-3