The super laceability of the hypercubes

The Spanning Connectivity of the Burnt Pancake Graphs

“…In biological informatics and neuroinformatics, the existence and structure of a w * -container signifies the cascade effect in signal transduction system and the reaction in a metabolic pathway. Recently, there are a lot studies on w * -container [2], [3], [11], [16], [19], [21], [24]. In this paper, we prove that the burnt pancake graph B n is super connected for n 2.…”

“…The corresponding concept of spanning connectivity in bipartite graphs is spanning laceability. A lot of interconnection networks are proved to be super spanning laceable [2], [3], [11], [15], [16], [19], [21], [23], [24]. The burnt pancake graphs B n was proposed by Gates and Papadimitriou [6].…”

One-to-Many Disjoint Path Covers in a Graph with Faulty Elements

“…(2) t 1 (2) (1) It is obvious that at least one of the above three are always applicable provided G has a general-demand k-DPC and w is chosen carefully. The difficulty here is how to pick up such a "proper" vertex w. It might not always be sufficient to pick up w in an arbitrary manner.…”

“…Oneto-one DPC's in recursive circulants [10,17] and hypercubes with faulty edges [2] were investigated. A one-to-one k-DPC is also known as a k * -container [2,17].…”

“…Oneto-one DPC's in recursive circulants [10,17] and hypercubes with faulty edges [2] were investigated. A one-to-one k-DPC is also known as a k * -container [2,17]. In hypercube-like interconnection networks, called restricted HL-graphs, with faulty vertices and/or edges, one-to-many DPC's [11], paired DPC's [14,15], and unpaired DPC's [12] were constructed.…”