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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)
The Heawood graph and K3;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 2factor hamiltonian graph then either G is a circuit or k 1⁄4 3: Furthermore, we construct an infinite family of cubic bipartite 2-factor hamiltonian graphs based on the Heawood(More)
For 3 ≤ k ≤ 20 with k 6= 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)
Let k, l,m, n, and μ be positive integers. A Zμ-scheme of valency (k, l) and order (m,n) is an m × n array (Sij) of subsets Sij ⊆ Zμ such that for each row and column one has ∑n j=1 |Sij | = k and ∑m i=1 |Sij | = l, respectively. Any such scheme is an algebraic equivalent of a (k, l)-semiregular bipartite voltage graph with n and m vertices in the(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 2factor and has minimum degree at least eight has two non-isomorphic 2factors. In addition we construct: an infinite family of strongly(More)