An isospin analysis of B → ππ decays yields sin 2α, where α is the usual CKM angle α ≡ arg[−V td V * tb /(V ud V * ub)] without hadronic uncertainty if isospin is a perfect symmetry. Yet isospin symmetry is broken not only by electroweak effects but also by the u and d quark mass difference — the latter drives π 0 − η, η ′ mixing and converts the isospin-perfect triangle relation between the B ...

A connected graph G is said to be factor-critical if G − v has a perfect matching for every vertex v of G. Lovász proved that every factor-critical graph has an ear decomposition. In this paper, the ear decomposition of the factor-critical graphs G satisfying that G− v has a unique perfect matching for any vertex v of G with degree at least 3 is characterized. From this, the number of maximum m...

We review a characterization of domination perfect graphs in terms of forbidden induced subgraphs obtained by Zverovich and Zverovich [12] using a computer code. Then we apply it to a problem of unique domination in graphs recently proposed by Fischermann and Volkmann. 1 Domination perfect graphs Let G be a graph. A set D ⊆ V (G) is a dominating set of G if each vertex of G either belongs to D ...

Given a simple graph G, a set C ⊆ V (G) is a neighborhood cover set if every edge and vertex of G belongs to some G[v] with v ∈ C, where G[v] denotes the subgraph of G induced by the closed neighborhood of the vertex v. Two elements of E(G)∪V (G) are neighborhood-independent if there is no vertex v ∈ V (G) such that both elements are in G[v]. A set S ⊆ V (G) ∪ E(G) is neighborhood-independent i...

Given a clustered graph (G,V), that is, a graph G = (V,E) together with a partition V of its vertex set, the selective coloring problem consists in choosing one vertex per cluster such that the chromatic number of the subgraph induced by the chosen vertices is minimum. This problem can be formulated as a covering problem with a 0-1 matrix M(G,V). Nevertheless, we observe that, given (G,V), it i...