Path between 2 non-directed graphs w/ non-empty intersection

mastriani

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Joined
Jul 3, 2018
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I have 2 un-direct graphs, A and B. I know that the intersection between A and B is not empty. In detail, suppose that s and d are nodes in A and that b is a node in B. I know that some nodes in I(b) (neighbors of b) and also their edges belong to A, but NOT b. Because I am looking for a path from s to d passing through b, I wish to prove that is plausible to insert the b node and its “restricted” set of edges ( E(I(b) in A) to the path. Any hint? Suggestion?
 

Dr.Peterson

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Nov 12, 2017
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I have 2 un-direct graphs, A and B. I know that the intersection between A and B is not empty. In detail, suppose that s and d are nodes in A and that b is a node in B. I know that some nodes in I(b) (neighbors of b) and also their edges belong to A, but NOT b. Because I am looking for a path from s to d passing through b, I wish to prove that is plausible to insert the b node and its “restricted” set of edges ( E(I(b) in A) to the path. Any hint? Suggestion?
I haven't worked with graphs in a long time, but it seems to me that you need more information. For example, are your graphs known to be connected? Also, I'm not sure you've clearly stated the theorem you want to prove. Is your statement about nodes in I(b) meant to be a given, or are you claiming that as implied? And can you fully define what you mean by I(b) and E(I(b))?
 
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