SCHUR’S COLOURING THEOREM FOR NONCOMMUTING PAIRS
نویسندگان
چکیده
منابع مشابه
A dichotomy theorem for circular colouring reconfiguration
Let p and q be positive integers with p/q ≥ 2. The “reconfiguration problem” for circular colourings asks, given two (p, q)-colourings f and g of a graph G, is it possible to transform f into g by changing the colour of one vertex at a time such that every intermediate mapping is a (p, q)-colouring? We show that this problem can be solved in polynomial time for 2 ≤ p/q < 4 and that it is PSPACE...
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We show that the maximum degree of a graph G is equal to theminimum number of ocm sets covering G, where an ocm set is the vertex-disjoint union of elementary odd cycles and onematching, and a collection of ocm sets covers G if every edge is in the matching of an ocm set or in some odd cycle of at least two ocm sets. © 2013 Elsevier B.V. All rights reserved.
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We prove the following theorem: if G is an edge-chromatic critical multigraph with more than 3 vertices, and if x, y are two adjacent vertices of G, the edge-chromatic number of G does not change if we add an extra edge joining x and y.
متن کاملBrooks' Vertex-Colouring Theorem in Linear Time
Brooks’ Theorem [R. L. Brooks, On Colouring the Nodes of a Network, Proc. Cambridge Philos. Soc. 37:194-197, 1941] states that every graph G with maximum degree ∆, has a vertex-colouring with ∆ colours, unless G is a complete graph or an odd cycle, in which case ∆ + 1 colours are required. Lovász [L. Lovász, Three short proofs in graph theory, J. Combin. Theory Ser. 19:269-271, 1975] gives an a...
متن کاملAbout a Brooks-type theorem for improper colouring
A graph is k-improperly -colourable if its vertices can be partitioned into parts such that each part induces a subgraph of maximum degree at most k. A result of Lovász states that for any graph G, such a partition exists if ≥ ⌈ Δ(G)+1 k+1 ⌉ . When k = 0, this bound can be reduced by ∗ This work was partially supported by the Égide eco-net project 16305SB. † Partially supported by the Brazilian...
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 2019
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972719000406