dipath

dipath

[′dī‚path]
(mathematics)
References in periodicals archive ?
MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is a dipath for every j [member of] {[j.
i] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] in [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], either [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] or [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] must be a dipath of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
i,j]), and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is a dipath of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], then [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] has to be a dipath of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
Proof: Similarly as for previous Claim 2, if the statement of the claim is not fulfilled by [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], then there is no dipath with length at most k joining any two of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] including the s([v.
Indeed, assume that having the dipath [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (resp.
H] that do not form a representative pair are joined by a dipath with length at most k.
Besides, there is a dipath with length at most k joining u' and any vertex v' from another gadget [G.
Furthermore, these three dipaths cannot be all directed from or towards the s([v.
Besides these three dipaths cannot be all directed from or towards the s([v.

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