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Even [a,b]-factors in graphs

Mekkia KouiderPreben Dahl Vestergaard — 2004

Discussiones Mathematicae Graph Theory

Let a and b be integers 4 ≤ a ≤ b. We give simple, sufficient conditions for graphs to contain an even [a,b]-factor. The conditions are on the order and on the minimum degree, or on the edge-connectivity of the graph.

Decomposition of multigraphs

Mekkia KouiderMaryvonne MahéoKrzysztof BryśZbigniew Lonc — 1998

Discussiones Mathematicae Graph Theory

In this note, we consider the problem of existence of an edge-decomposition of a multigraph into isomorphic copies of 2-edge paths K 1 , 2 . We find necessary and sufficient conditions for such a decomposition of a multigraph H to exist when (i) either H does not have incident multiple edges or (ii) multiplicities of the edges in H are not greater than two. In particular, we answer a problem stated by Z. Skupień.

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