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A simple graphG is said to be fractionaln-factor-critical if after deleting anyn vertices the remaining subgraph still has a fractional perfect matching . For fractionaln-factor-criticality ...
) are shown in Table 1, and bulk statistics (see Statistical analysis of vectors) are shown in Table 2. Example inputs (plasma- or endothelial-labeled fluorescent images) and intermediates (energy, size, vertex ...
to this in Subsection 2.5. The notion of Morse matchings with critical faces subsumes Whitehead's notion of collapses. Recall that a perfect Morse matching $$\varPhi$$ on a regular CW complex $$C$$ is a Morse matching ...
particle is bound to a neighbouring particle. This is known as a perfect matching . Describing the physics of this system amounts to counting the number of perfect matchings , subject to certain boundary ...
graph metrics, such as betweenness centrality, to determine which edges to delete . Relatedly, [13] studies grid vulnerability based on various graph edge and vertex deletion scenarios; they conclude ...
$| vertices with girth at least |$g$|. Let |$v$| be any vertex of |$G$| and let |$u_1,u_2$| be two of its neighbors. Let |$H$| be the graph obtained by deleting the edges |$vu_1$| and |$vu_2$| and adding ...
of computers in poorly structured networks can cause networks to disconnect and fail. It is desirable that the graph remains connected after vertex deletion . Obviously, this can only be guaranteed if the number ...
was perfect at all coverage rates. For distances of 0.75% and below, the vast majority of the reconstructed haplotypes still perfectly match a true haplotype. In general, the false positive rate decreases ...
) at a given vertex is linear in the worst case. However, as each vertex has an unlimited number of incoming deletion edges, an appropriate restriction of the search space should be considered. In the following ...
longstanding problems. Roughly speaking, a graph is robustly expanding if it still expands after the deletion of a small fraction of its vertices and edges. Our main result allows us to harness the useful ...
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