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- W4300692764 abstract "A symmetric $mtimes m$ matrix $M$ with entries taken from ${0,1,ast}$ gives rise to a graph partition problem, asking whether a graph can be partitioned into $m$ vertex sets matched to the rows (and corresponding columns) of $M$ such that, if $M_{ij}=1$, then any two vertices between the corresponding vertex sets are joined by an edge, and if $M_{ij}=0$ then any two vertices between the corresponding vertex sets are not joined by an edge. The entry $ast$ places no restriction on the edges between the corresponding sets. This problem generalises graph colouring and graph homomorphism problems. A graph with no $M$-partition but such that every proper subgraph does have an $M$-partition is called a minimal obstruction. Feder, Hell and Xie have defined friendly matrices and shown that non-friendly matrices have infinitely many minimal obstructions. They showed through examples that friendly matrices can have finitely or infinitely many minimal obstructions and gave an example of a friendly matrix with an NP-hard partition problem. Here we show that almost all friendly matrices have infinitely many minimal obstructions and an NP-hard partition problem." @default.
- W4300692764 created "2022-10-04" @default.
- W4300692764 creator A5007725876 @default.
- W4300692764 date "2014-03-14" @default.
- W4300692764 modified "2023-10-06" @default.
- W4300692764 title "Almost all friendly matrices have many obstructions" @default.
- W4300692764 doi "https://doi.org/10.48550/arxiv.1403.3548" @default.
- W4300692764 hasPublicationYear "2014" @default.
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