Timeline for Generalized concept of subgraph (input/output graphs)
Current License: CC BY-SA 3.0
3 events
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| Aug 10, 2017 at 18:50 | comment | added | Mark Fischler | A related definition which is a graph, and a problem which is not completely trivial involving that definition". * Define a "1-indirect vertex induced subgraph of graph $G = (V,E)$ induced by $U\subset V$ to have edge-set $F$ of exactly those edges with at least one vertex in $U$, and vertex set $W$ consisting of those vertices touched by a member of $F$. * The nontrivial problem is: Find a graph $G$ and subset $U$ of its vertices such that the 1-indirect vertex-induced subgraph of $G$ by $U$ has greater chromatic number than that of the vertex-induced subgraph of $G$ by $U$. | |
| Aug 10, 2017 at 18:22 | comment | added | Peter Heinig | Not an answer if your question is contrued strictly, yet the following two things are tagentially relevant: (1) it is very usual to consider boundaries of vertex sets, in the sense of sets of edges with exactly one end in the given vertex set, and of course you can cobble together a "definition" from this concept of 'boundary' and the usual 'ordinary subgraph'. (2) when working with e.g. string diagrams and operads, a concept of half-edges exists. I have not seen your idea addressed as such. | |
| Aug 10, 2017 at 18:03 | history | asked | Hans-Peter Stricker | CC BY-SA 3.0 |