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- W3021839791 abstract "(joint work with M.Abreu, J. Goedgebeur, G. Mazzuoccolo) A emph{$k$--bisection} of a bridgeless cubic graph $G$ is a $2$--colouring of its vertex set such that the colour classes have the same cardinality and all connected components in the two subgraphs induced by the colour classes ({em monochromatic components} in what follows) have order at most $k$.Ban and Linial conjectured that {em every bridgeless cubic graph admits a $2$--bisection except for the Petersen graph}.A similar problem for the edge set of cubic graphs has been studied: Wormald conjectured that {em every cubic graph $G$ with $|E(G)| equiv 0 , mod , 2$ has a $2$--edge colouring such that the two monochromatic subgraphs are isomorphic linear forests} (i.e. a forest whose components are paths).%(A {em linear forest} is a forest whose components are paths and a {em linear partition} of a graph $G$ is a partition of its edge set into linear forests.)%(A {em linear forest} is a forest whose components are paths).Finally, Ando conjectured that {em every cubic graph admits a bisection such that the two induced monochromatic subgraphs are isomorphic.} In this paper, we deal with these conjectures by giving a detailed insight into the conjecture of Ban--Linial and of Wormald and provide evidence of a strong relation of both of them with Ando's conjecture. Furthermore, we also give computational and theoretical evidence in their support. As a result, we pose some open problems stronger than the above cited conjectures. Moreover, we prove Ban--Linial's conjecture for cubic cycle permutation graphs. As a by--product, of studying $2$--edge colourings of cubic graphs having linear forests as monochromatic components, we give a negative answer to a problem posed by Jackson and Wormald about certain decompositions of cubic graphs into linear forests." @default.
- W3021839791 created "2020-05-13" @default.
- W3021839791 creator A5000737515 @default.
- W3021839791 date "2017-05-30" @default.
- W3021839791 modified "2023-09-27" @default.
- W3021839791 title "Colourings of cubic graphs inducing isomorphic monochromatic subgraphs" @default.
- W3021839791 hasPublicationYear "2017" @default.
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