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Forest characterization
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forestcharacterizationstackoverflow
Problem
Prove that each property below characterizes forests...
a. every induced subgraph has a vertex of degree at most one.
When proving a characterization, do we have to prove both directions, like an if and only if, or does it suffice to prove only one direction?
a. every induced subgraph has a vertex of degree at most one.
When proving a characterization, do we have to prove both directions, like an if and only if, or does it suffice to prove only one direction?
Solution
"Characterize" means you must prove both directions.
However, you can be more efficient with multiple characterizations: proving A implies B implies C implies A shows all three are equivalent, because implication is transitive. Examples in practice:
Equivalence of induction, strong induction, and well-ordering
Equivalence of 6 different characterizations of the exponential function
However, you can be more efficient with multiple characterizations: proving A implies B implies C implies A shows all three are equivalent, because implication is transitive. Examples in practice:
Equivalence of induction, strong induction, and well-ordering
Equivalence of 6 different characterizations of the exponential function
Context
StackExchange Computer Science Q#130990, answer score: 2
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