Abstract
AbstractA simple graph with edge‐connectivity and minimum degree is maximally edge‐connected if . In 1964, given a nonincreasing degree sequence , Jack Edmonds showed that there is a realization of that is ‐edge‐connected if and only if with when . We strengthen Edmonds's result by showing that given a realization of if is a spanning subgraph of with such that when , then there is a maximally edge‐connected realization of with as a subgraph. Our theorem tells us that there is a maximally edge‐connected realization of that differs from by at most edges. For , if has a spanning forest with components, then our theorem says there is a maximally edge‐connected realization that differs from by at most edges. As an application we combine our work with Kundu's ‐factor theorem to show there is a maximally edge‐connected realization with a ‐factor for and present a partial result to a conjecture that strengthens the regular case of Kundu's ‐factor theorem.
Published Version
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