Some Transfinite Graph Theory
A peculiarity of transfinite graphs not encountered in conventional graphs is that connectedness by means of paths need not be transitive as a binary relationship between branches. In Section 3.1, we establish a criterion (Condition 3.1-2) under which transfinite connectedness through paths is transitive. The proof of this is far simpler in the present context of pristine graphs than it is for general transfinite graphs [34, Chapter 3]. Moreover, the present criterion combines the two separate ones given in [34, Conditions 3.2-1 and 3.5-1].
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