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Let G be a 2k‐edge‐connected graph with and let for every . A spanning subgraph F of G is called an L‐factor, if for every . In this article, we show that if for every , then G has a k‐edge‐connected L‐factor. We also show that if and for every , then G has a k‐edge‐connected L‐factor.
The square of a graph G denoted by G2, is the graph with the same vertex set as G and edges linking pairs of vertices at distance at most 2 in G. The chromatic number of the square of the Cartesian product of two cycles was previously determined for some cases. In this paper, we determine the precise value of χ((Cm□Cn)2) for all the remaining cases. We show that for all ordered pairs (m,n) except...
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