Timeline for Cores of infinite graphs
Current License: CC BY-SA 3.0
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| Dec 2, 2014 at 20:01 | comment | added | Goldstern | MR1322084 (96c:05175) Bauslaugh, B. Core-like properties of infinite graphs and structures. "[...]The question of which property of infinite graphs should be used as the definition of core thus arises. The relationship between various candidate properties is explored and completely described." Also Bodirsky's thesis may be of interest: $\omega$-categorical structures always have a core. urn:nbn:de:0296-matheon-2754 opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/275 | |
| Dec 2, 2014 at 12:09 | comment | added | Eric Wofsey | These are both pretty trivially false for the equivalence class of the complete graph. To get something that has any hope of being true, you need to account for the fact that infinite sets have endomorphisms that are injective but not surjective. For instance, in (1) you should replace "smallest cardinality" with something like "isomorphic to any subgraph that is equivalent to it" (or maybe "embeds in every subgraph that is equivalent to it") and in (2) you should replace "isomorphism" with "injection". | |
| Dec 2, 2014 at 11:28 | history | asked | Dominic van der Zypen | CC BY-SA 3.0 |