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Search: Posts Made By: R.D. Silverman
Forum: Puzzles 2020-04-10, 12:14
Replies: 44
Views: 6,383
Posted By R.D. Silverman
One can cut down the search further. If the...

One can cut down the search further. If the complete graph on n nodes does not exceed
.70 then one can skip searching the n node graphs. Generating the n+1 node graphs
can/should be made easier...
Forum: Puzzles 2020-04-03, 13:29
Replies: 44
Views: 6,383
Posted By R.D. Silverman
The issue is not the labeling. It is assumed that...

The issue is not the labeling. It is assumed that A is the person infected at t=0.
The question is where A is placed on the graph.





I disagree. I think this is the easy part.
Forum: Puzzles 2020-04-03, 08:38
Replies: 44
Views: 6,383
Posted By R.D. Silverman
Consider the following graph: ...

Consider the following graph:

A-----B-------C

vs.

B-----A------C

If the infected person is A he/she can infect two people on the first iteration in the second
graph, but not the first.
Forum: Puzzles 2020-04-02, 03:09
Replies: 44
Views: 6,383
Posted By R.D. Silverman
We agree. But I seek a formal proof.

We agree. But I seek a formal proof.
Forum: Puzzles 2020-04-02, 03:06
Replies: 44
Views: 6,383
Posted By R.D. Silverman
Actually it is much less, because we are only...

Actually it is much less, because we are only need consider labelled connected graphs.
There are less than 2000000 such with 8 nodes. See http://oeis.org/A001187
Forum: Puzzles 2020-04-02, 02:29
Replies: 44
Views: 6,383
Posted By R.D. Silverman
Thank you. I misread the problem as ">=...

Thank you. I misread the problem as ">= 70.00%".
Forum: Puzzles 2020-04-02, 02:07
Replies: 44
Views: 6,383
Posted By R.D. Silverman
BTW, there is a reason why .70 was selected. ...

BTW, there is a reason why .70 was selected. (1-1/e) should be familiar to participants
herein.

Another interesting question. Among all graphs, which is maximal? I think I know the answer.
Forum: Puzzles 2020-04-02, 01:59
Replies: 44
Views: 6,383
Posted By R.D. Silverman
I think the correct approach to a proof is to...

I think the correct approach to a proof is to model the problem as a stochastic
process/martingale. I wish I could remember the material..... Its been 45 years
since I last looked at/took a...
Forum: Puzzles 2020-04-02, 01:52
Replies: 44
Views: 6,383
Posted By R.D. Silverman
But the labeling is arbitrary... Any node for a...

But the labeling is arbitrary... Any node for a given graph can be labeled 'A'.

An interesting question: Given a graph X. Delete an edge. Prove or disprove that
the resulting graph always...
Forum: Puzzles 2020-04-01, 22:33
Replies: 44
Views: 6,383
Posted By R.D. Silverman
Also: Is it possible to infect more than one...

Also:

Is it possible to infect more than one person in a time period??
Forum: Puzzles 2020-04-01, 22:19
Replies: 44
Views: 6,383
Posted By R.D. Silverman
HUH? This problem seems very under-posed! ...

HUH?

This problem seems very under-posed! Some questions:

(1) What are the initial conditions? If all are healthy at t=0, then they remain healthy.
(if one is adjacent to 2 rather than 3...
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