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The structure and existence of 2-factors in iterated line graphs

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Ferrara M., Gould R., Hartke S.

Discussiones Mathematicae Graph Theory

2007

tom 27

nr 3

507-526

We prove several results about the structure of 2-factors in iterated line graphs. Specifically, we give degree conditions on G that ensure L²(G) contains a 2-factor with every possible number of cycles, and we give a sufficient condition for the existence of a 2-factor in L²(G) with all cycle lengths specified. We also give a characterization of the graphs G where $L^k(G)$ contains a 2-factor.

Potentially H-bigraphic sequences

100%

Ferrara M., Jacobson M., Schmitt J., Siggers M.

Discussiones Mathematicae Graph Theory

2009

tom 29

nr 3

583-596

We extend the notion of a potentially H-graphic sequence as follows. Let A and B be nonnegative integer sequences. The sequence pair S = (A,B) is said to be bigraphic if there is some bipartite graph G = (X ∪ Y,E) such that A and B are the degrees of the vertices in X and Y, respectively. If S is a bigraphic pair, let σ(S) denote the sum of the terms in A. Given a bigraphic pair S, and a fixed bipartite graph H, we say that S is potentially H-bigraphic if there is some realization of S containing H as a subgraph. We define σ(H,m,n) to be the minimum integer k such that every bigraphic pair S = (A,B) with |A| = m, |B| = n and σ(S) ≥ k is potentially H-bigraphic. In this paper, we determine $σ(K_{s,t},m,n)$, σ(Pₜ,m,n) and $σ(C_{2t},m,n)$.

Ograniczanie wyników

2 Discussiones Mathematicae Graph Theory

2 Ferrara M.

1 Gould R.

1 Hartke S.

1 Jacobson M.

1 Schmitt J.

1 Siggers M.

1 2009

1 2007

Wyniki wyszukiwania

The structure and existence of 2-factors in iterated line graphs

Potentially H-bigraphic sequences