Assume we have a class of graphs. Now what does this sentence mean?
"each of the graphs in the class, monotonically should make no difference".
Dear Peter,
I made it in a better way :)
But, I have not received your final answer of my previous question yet.
It is still open.
Dear Peter,
This sentence has not made by me.
I have received this sentence from one other scientist.
That's why I also do not understand the meaning :)
Is there anyone here who can understand the meaning of the mentioned sentence?
Ok, I think the answer is this:
A graph peoperty is monoton if every subgraph of a graph with property P, also has the property P. Same as bipartite graphs. every subgraph (Withot isolated vertices), of a bipartite graph is also bipartite.
Now, the meaning of "Monotonically should make no difference" is, for each of the graphs G in the class, if H is a subgraph of G, then H should have the same properties as G.
@Nazanin "A graph peoperty is monoton if every subgraph of a graph with property P, also has the property P" is called "hereditary property".
As for the original (part of a) sentence: if we join it to another domain of mathematics, it makes sense such as it is, despite imprecise wording: e.g. in a class of exponential functions with a basis a>1...
@Viera, thank you for your explanation. I think monotone and hereditary are both same. Please look at here:
https://en.wikipedia.org/wiki/Graph_property
The "Properties of properties" part.
@Peter, thanks for your helps. It is not in Italic. So we should think more about the meaning. But I think my explanation is 70% correct.
Please send me your ideas in case of any new explanation.
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