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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We prove that every internally 4-connected non-planar bipartite graph has an odd K3,3 subdivision; that is, a subgraph obtained from K3,3 by replacing its edges by internally disjoint odd paths with the same ends. The proof gives rise to a polynomial-time algorithm to find such a subdivision. (A bipartite graph G is internally 4-connected if it is 3-connected, has at least five vertices, and th...
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A permutation graph is a cubic graph admitting a 1-factor M whose complement consists of two chordless cycles. Extending results of Ellingham and of Goldwasser and Zhang, we prove that if e is an edge of M such that every 4-cycle containing an edge of M contains e, then e is contained in a subdivision of the Petersen graph of a special type. In particular, if the graph is cyclically 5-edge-conn...
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In this paper, we proved the following result: Let G be a (k + 2)-connected, non-(k − 3)apex graph where k ≥ 2. If G contains three k-cliques, say L1, L2, L3, such that |Li ∩ Lj| ≤ k − 2(1 ≤ i < j ≤ 3), then G contains a Kk+2 as a minor. Note that a graph G is t-apex if G− X is planar for some subset X ⊆ V (G) of order at most t . This theorem generalizes some earlier results by Robertson, Seym...
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ژورنال
عنوان ژورنال: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
سال: 2012
ISSN: 0025-5858,1865-8784
DOI: 10.1007/s12188-012-0063-x