Induced subgraph

The determination of all 2-embeddable (r, )-polycycles, i.e. ones whose skeleton can be embedded into a hypercube with scale 1 or 2. All parabolic and hyperbolic (r, )-polycycles are 2-embeddable and a characterization, by induced subgraphs, of such elliptic (r, < )-polycycles is presented. 

Theorem 833 ([DeSt02a])A (3,5)-polycycle different from Icosahedron 3,5 and 3,5 — v (Icosahedron with one vertex removed) is 2-embeddable if and only if it does not contain, as an induced subgraph, any of (3,5)-polycycles c3 and d + e2+d shown in Figure 8.4. 

In words, y is a subgraph, a closed subgraph, an induced subgraph of y, respectively, if this holds for any two chosen elements y and y of these orbits and suitable embeddings 0. 

Assume now that c belongs to C. Let D be the maximal induced subgraph of G defined in a way identical to how we defined C, with the difference being that we start with the vertex b instead of a, and follow the colors 2 and 4 instead of the colors 1 and 3. Again, if the vertex d does not belong to D, then we re-color D by swapping colors 2 and 4 and then color x with the color 2. 

The intuition behind this definition is that we relax the conditions of the Horn case by allowing some of the coloring lists to be empty. One can think of Hom+ (T, G) as a simplicial structure imposed on the set of all partial graph homomorphisms from T to G, i.e., graph homomorphisms from an induced subgraph of T to the graph G. 

Call a polycycle proper if it is apartial subgraph of r, q) and a helicene, otherwise (this term will be justified later by Theorem 4.3.1). Call a proper (r, )-polycycle induced (moreover, isometric) if this subgraph is, in addition, an induced (moreover, isometric) subgraph of r, q). Another interesting possible property of aptoper (r, q)-polycycle is being convex in r, q (see Section 4.4). 

In the previous section we introduced subgraphs and subgraphs induced by sets of nodes. Here, we extend these definitions to molecular graphs, recalUng that molecular graphs are unlabeled and colored multigraphs. 

Consider the subgraph of the underlying graph of the Hasse diagram of P Q induced by W U u W). Orient its edges as described above, i.e., they should... 

Assume that we have S C M such that S can be written as a direct product S = Si X S2 X X St. Assume furthermore that the subgraph of B induced by S is precisely the 1-skeleton of the corresponding cell. 

Finally, this label should be different for different ds, since otherwise, by the same argument as above, we would get more edges in the subgraph of F induced by S than what we allowed by om assiunptions. 

If the threshold is raised, to say S, > 0.90, the subset of compounds remains linked, but the subgraph induced by tlie higher threshold no longer forms a clique and c Cpd-5, of course, remains an isolated node. In this case, the adjacency matrix simplifies to... 

The graph of reaction distances constructed over the family 3Fp can be substantially reduced by deleting all vertices that are represented by forbidden S-graphs, i.e. the resulting subgraph, denoted 5p is induced by the union of subfamilies 3Fp u this subgraph of will be called reduced graph of reaction distances. 

Let Ga Va,Ea) be the subgraph induced by 14, where the execution delays of all data-dependent delay vertices assume the minimum value of zero. 

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