Inspired by the paper [10], using better differential characteristics in the biclique construction, we give another balanced biclique attack on full rounds PRINCE with the lower complexity in this paper. Our balanced biclique attack has 62.67 2 computational complexity and 32 2 data complexity. Furthermore, we first illustrate a star-based biclique attack on full rounds PRINCE cipher in this pa...

Throughout the paper all graphs G = (V,E) are undirected and simple. An induced biclique of G is a complete bipartite induced subgraph of G. A noninduced biclique is a complete bipartite (not necessarily induced) subgraph of G. Equivalently, the pair (X, Y ) of disjoint vertex subsets X ⊆ V and Y ⊆ V is a non-induced biclique of G if {x, y} ∈ E for all x ∈ X and y ∈ Y . If, additionally, X and ...

A graph is biclique-Helly when its family of (maximal) bicliques is a Helly family. We describe characterizations for biclique-Helly graphs, leading to polynomial time recognition algorithms. In addition, we relate biclique-Helly graphs to the classes of clique-Helly, disk-Helly and neighborhood-Helly graphs.

A biclique is a set of vertices that induce a bipartite complete graph. A graph G is biclique-Helly when its family of maximal bicliques satisfies the Helly property. If every induced subgraph of G is also biclique-Helly, then G is hereditary biclique-Helly. A graph is C4-dominated when every cycle of length 4 contains a vertex that is dominated by the vertex of the cycle that is not adjacent t...

A biclique of a graph G is an induced complete bipartite graph. A star of G is a biclique contained in the closed neighborhood of a vertex. A star (biclique) k-coloring of G is a k-coloring of G that contains no monochromatic maximal stars (bicliques). Similarly, for a list assignment L of G, a star (biclique) L-coloring is an L-coloring of G in which no maximal star (biclique) is monochromatic...

A co-biclique of a simple undirected graph G = (V, E) is the edge-set of two disjoint complete subgraphs of G. (A co-biclique is the complement of a biclique.) A subset F ⊆ E is an independent of G if there is a co-biclique B such that F ⊆ B, otherwise F is a dependent of G. This paper describes the minimal dependents of G. (A minimal dependent is a dependent C such that any proper subset of C ...

For a graph G, a biclique edge partition SBP(G) is a collection of bicliques (complete bipartite subgraphs) Bi such that each edge of G is contained in exactly one Bi. The Minimum Biclique Edge Partition Problem (MBEPP) asks for SBP(G) with the minimum size. In this paper, we show that for arbitrary small > 0, (6053/6052 − )-approximation of MBEPP is NP-hard. key words: biclique, edge partition...

MOTIVATION The O-ring theory reveals that the binding hot spot at a protein interface is surrounded by a ring of residues that are energetically less important than the residues in the hot spot. As this ring of residues is served to occlude water molecules from the hot spot, the O-ring theory is also called 'water exclusion' hypothesis. We propose a 'double water exclusion' hypothesis to refine...

The biclique cover number (resp. biclique partition number) of a graph G, bc(G) (resp. bp(G)), is the least number of bicliques—complete bipartite subgraphs—that are needed to cover (resp. partition) the edges of G. The local biclique cover number (resp. local biclique partition number) of a graph G, lbc(G) (resp. lbp(G)), is the least r such that there is a cover (resp. partition) of the edges...