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The Heawood graph and K 3;3 have the property that all of their 2-factors are Hamilton circuits. We call such graphs 2-factor hamiltonian. We prove that if G is a k-regular bipartite 2-factor hamiltonian graph then either G is a circuit or k ¼ 3: Furthermore, we construct an infinite family of cubic bipartite 2-factor hamiltonian graphs based on the Heawood… (More)

- M. Funk
- 2010

For 3 ≤ k ≤ 20 with k = 4, 8, 12, all the smallest currently known k–regular graphs of girth 5 have the same orders as the girth 5 graphs obtained by the following construction: take a (not necessarily Desarguesian) elliptic semiplane S of order n − 1 where n = k − r for some r ≥ 1; the Levi graph Γ (S) of S is an n–regular graph of girth 6; parallel… (More)

Although small ubiquitin-like modifier (SUMO) is conjugated to proteins involved in diverse cellular processes, the functional analysis of SUMOylated proteins is often hampered by low levels of specific SUMOylated proteins in the cell. Here we describe a SUMO-conjugating enzyme (Ubc9) fusion-directed SUMOylation (UFDS) system, which allows efficient and… (More)

Constitutive and induced protein SUMOylation is involved in the regulation of a variety of cellular processes, such as regulation of gene expression and protein transport, and proceeds mainly in the nucleus of the cell. So far, several hundred SUMOylation targets have been identified, but presumably they represent only a part of the total of proteins which… (More)

The Heawood graph and K 3,3 have the property that all of their 2–factors are hamiltonian cycles. We call such graphs 2–factor hamiltonian. More generally, we say that a connected k–regular bipartite graph G belongs to the class BU(k) if for each pair of 2-factors, F 1 , F 2 in G, F 1 and F 2 are isomorphic. We prove that if G ∈ BU(k) , then either G is a… (More)

Let G be a connected k–regular bipartite graph with bipartition V (G) = X ∪Y and adjacency matrix A. We say G is det–extremal if per(A) = |det(A)|. Det–extremal k–regular bipartite graphs exist only for k = 2 or 3. McCuaig has characterized the det–extremal 3–connected cubic bipartite graphs. We extend McCuaig's result by determining the structure of… (More)

We show that a digraph which contains a directed 2-factor and has minimum in-degree and out-degree at least four has two non-isomorphic directed 2-factors. As a corollary we deduce that every graph which contains a 2-factor and has minimum degree at least eight has two non-isomorphic 2-factors. In addition we construct: an infinite family of strongly… (More)