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Showing 1 to 14 of 14 for “"minimum rank"”.
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The Minimum Rank Problem Over Finite Fields
… minimal forbidden subgraph for the graphs having minimum rank at most 3 over the finite field of order 2. We also list all 62 such minimal forbidden subgraphs and show that many of these are minimal forbidden subgraphs for any field. Our second main result is a structural characterization of all …
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On the minimum rank of certain graphs with path cover number 2
The minimum rank problem is an interesting and ongoing problem in spectral graph theory which seeks to answer the question "Given a simple graph G what is the minimum rank of a matrix whose off-diagonal zero/nonzero pattern is described by G?" In recent years, the minimum rank of trees, unicyclic …
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On a graph parameter related to vertex labelings and its application to minimum rank problems in graph theory
This thesis regards the minimum rank and minimum positive semidefinite rank of a simple graph. A graph parameter, called the minimum labeling degree (mld), is defined in terms of the concept of a vertex labeling of a graph, and its value is calculated for a few graph classes. It is proved here that …
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On the δ-conjecture for graphs with minimum degree |G| – 4
For a graph G of order n, the minimum rank of G is defined to be the minimum rank among all n × n symmetric matrices whose ij-entry is nonzero precisely when {i, j} is an edge of G. The delta conjecture proposes a relationship between the minimum rank and the minimum degree of a given graph. We …
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A Vascular and Non-Vascular Flora of the McGee Creek Watershed, Mono County, California
… (774 vascular, 196 non-vascular) and 1011 minimum-rank taxa (813 vascular, 198 nonvascular). Eighty-three percent of these species (84% of the minimum-rank taxa), including 93% of the rare or threatened species and 93% of the introduced species, were not documented within the watershed …
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A Vascular Flora of the Nopah Range, Inyo County, California
… documenting 60 families, 198 genera, and 365 minimum-rank vascular plant taxa present in the study area. Twenty-nine minimum-rank taxa are listed as rare in California and 32 appear to have edaphic affinities, mainly to the abundant carbonate substrates present in the Nopah Range such as …
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Vascular Floristic Study of the Piute Mountains, Kern County, California
… herbarium collections representing 704 minimum-rank taxa (species, subspecies, varieties, named hybrids). Despite previous botanical work, there were large spatial and temporal gaps in the collection history of the Piute Mountains, and many species collected in the past had not been …
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A Vascular Flora of the Sacatar Trail Wilderness, Sierra Nevada, California
… the Sacatar Trail Wilderness that includes 507 minimum-rank taxa from 74 plant families. Over half of the checklist (266 minimum-rank taxa) were newly documented within the study area including 21 new county records. Twenty-four special-status (rare) taxa were observed, as well as 32 non-native …
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A Flora of the Silver Peak Range, Esmeralda County, Nevada
… survey over the course of 2.5 years yielded 640 minimum rank taxa, about 339 of which were previously undocumented in the range. Of these, 3 were new to the state of Nevada, 49 were new to Esmeralda County, 56 were species of conservation concern, and 52 were non-native taxa.</p>
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The Relationship Between the Minimal Rank of a Tree and the Rank-Spreads of the Vertices and Edges
… to the edges of G. Let mr(F,G)be the minimum rank over all matrices in S(F,G). We give a field independent proof of a well-known result that for a tree the sum of its path cover number and minimal rank is equal to the number of vertices in the tree. The rank-spread of a vertex v of G …
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A Flora of Coyote Ridge and Flat, Inyo County, California
… 2019 and August 2021 documented a total of 543 minimum-rank taxa, 273 of which were not previously known to the area. New collections and examination of historical specimens have yielded occurrences of 12 new rare plants for the area including new records for the Sierra Nevada mountains and one …
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A Vascular Flora of the Manter and Salmon Creek Watersheds, Tulare County, California
… of 1,412 plant specimens. A total of 590 minimum-rank taxa were documented in the study area, representing 78 families and 270 genera. Of the minimum-ranked taxa, 34 are non-native and 28 have conservation status. Angelica callii , a California endemic with a California Rare Plant Ranking …
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Dense Optical Flow Estimation using Diffusion Distances
… are based on both the maximum correlation and minimum rank of correlation vectors from the correlation matrix. A large number of very accurate estimates, spread through the image can be identified based on level of consensus with the estimates from surrounding pixels, which we term as …
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Efficient and guaranteed algorithms for sparse inverse problems
… Feng and Bresler, provides a guarantee with the minimum number of measurements. We focus instead on the unfavorable but practically significant case of rank defect or ill-conditioning. This situation arises with a limited number of measurement vectors, or with highly correlated signal components. …