A node of V1 is adjacent to a node of V2 if and only if the corresponding vertices of G are either the same or adjacent. Then X and Y are adjacent if and only if H has a perfect matching. The existence of a perfect matching in a bipartite graph can be verified in polynomial time...
Invoking the Schmidt decomposition, self-testing all bipartite entangled states reduces to self-testing all states of the form. where 0<ci<1 for all i and . One may wonder whether mixed states could also be self-tested, that is, if some P(a, b|x, y) is uniquely compatible with a ...
Network graphs were calculated based on the correlation of the abundance of all the tested genera using the R package ggClusterNet [24], which could complete the whole microbiome and bipartite network analysis from correlations calculation, network visualisation, network properties calculation, and node...
Prove that a complete graph (a graph in which there is an edge between every pair of vertices) has n^(n-2) spanning trees. Here n is the number of vertices in the graph. Use mathematical induction to show that recurrence T(n) = T(n-1) ...
On vertex stability with regard to complete bipartite subgraphs Summary: A graph $G$ is called $(H; k)$-vertex stable if $G$ contains a subgraph isomorphic to $H$ ever after removing any of its $k$ vertices. $Q(H; k)$ denotes the minimum size among the sizes of all $(H; k)$...
Generally, SRUS data must be acquired over a certain period depending on ultrasound equipment, acquisition technique, and vascular bed to obtain enough MB detections to generate a complete (or near-complete) image of the vasculature [32,33,34,35]. The MB velocities are typically calculated from...