Closed subgraph

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. 

DEFINITION A subgraph G of G is zero exit or closed if no arrow leaves G it is zero entry if no arrows enter G. ... 

Proof. Assume (i) and (ii) hold, and take a closed cycle c in P. The set of elementary polycycles, passed by c, is a finite connected subgraph Majc(P) of Maj(P), so also a tree. If c pass though only one elementary component, then, by (i),... 

In 1943, Hadwiger stated a conjecture closely related to the four-color theorem. Recall that a graph H is called a minor of another graph G if H can be obtained from a subgraph of G by a sequence of edge-contractions. 

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