Toroidal graphs containing neither K5− nor 6-cycles are 4-choosable
نویسندگان
چکیده
منابع مشابه
K5-Subdivisions in graphs containing K-4
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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In this paper, we prove that planar graphs without 4, 5 and 8-cycles are acyclically 4-choosable.
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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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متن کاملA Note on (3, 1)∗-Choosable Toroidal Graphs
An (L, d)∗-coloring is a mapping φ that assigns a color φ(v) ∈ L(v) to each vertex v ∈ V (G) such that at most d neighbors of v receive colore φ(v). A graph is called (m, d)∗-choosable, if G admits an (L, d)∗-coloring for every list assignment L with |L(v)| ≥ m for all v ∈ V (G). In this note, it is proved that every toroidal graph, which contains no adjacent triangles and contains no 6-cycles ...
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ژورنال
عنوان ژورنال: Journal of Graph Theory
سال: 2016
ISSN: 0364-9024
DOI: 10.1002/jgt.22054