Geometrical constraints on Bennett's predictions of chromosome order

Dorninger, Dietmar; Timischl, Werner

doi:10.1038/hdy.1987.138

Cited by 44 publications

(15 citation statements)

References 4 publications

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“…In the last few years a great number of problems have been dealt with in terms of edge-colored graphs for modeling purposes, as well as for theoretical investigation [3,[7][8][9]18,23]. Previous work on the subject has focused on the determination of particular properly edge-colored subgraphs, such as Hamiltonian or Eulerian configurations, colored in a specified pattern [1,2,[4][5][6]10,21,22,25,27], that is, subgraphs such that adjacent edges have different colors.…”

Section: Introduction Notation and Terminologymentioning

confidence: 99%

Paths and trails in edge-colored graphs

Abouelaoualim

Das

Faria

et al. 2008

Theoretical Computer Science

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a b s t r a c tThis paper deals with the existence and search for properly edge-colored paths/trails between two, not necessarily distinct, vertices s and t in an edge-colored graph from an algorithmic perspective. First we show that several versions of the s − t path/trail problem have polynomial solutions including the shortest path/trail case. We give polynomial algorithms for finding a longest properly edge-colored path/trail between s and t for a particular class of graphs and characterize edge-colored graphs without properly edgecolored closed trails. Next, we prove that deciding whether there exist k pairwise vertex/edge disjoint properly edge-colored s − t paths/trails in a c-edge-colored graph G c is NP-complete even for k = 2 and c = Ω(n 2 ), where n denotes the number of vertices in G c . Moreover, we prove that these problems remain NP-complete for c-edgecolored graphs containing no properly edge-colored cycles and c = Ω(n). We obtain some approximation results for those maximization problems together with polynomial results for some particular classes of edge-colored graphs.

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Section: Introduction Notation and Terminologymentioning

confidence: 99%

Paths and trails in edge-colored graphs

Abouelaoualim

Das

Faria

et al. 2008

Theoretical Computer Science

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“…A specific order of the chromosomes within the 203 genome of H vulgare, as reported by Bennett (1982Bennett ( , 1983Bennett ( , 1984a and Heslop-Harrison & Bennett (1983a,b, 1984, was not found by us (Linde-Laursen & Jensen, 1984). In addition, the validity of the finding and its theoretical and statistical bases have been questioned (Coates & Smith, 1984;Callow, 1985;John et al, 1985;Dorninger & Timischl, 1987;Rawlins & Shaw, 1988).…”

Section: Introductionmentioning

confidence: 69%

Genome and chromosome disposition at somatic metaphase in a Hordeum × Psathyrostachys hybrid

Linde‐Laursen

Jensen

1991

Heredity

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The distribution of chromosomes by centromeres and telomeres was studied in 100 squashed, somatic metaphases of a Hordeum vulgare (2 n =2x = 14) x Psathyrostachys fragilis (2 n = 2x = 14)hybrid. The chromosomes and chromosome arms were individually identified in each of the parental genomes by their Giemsa C-banding patterns. The P. fragilis chromosomes were more widely scattered on the metaphase plate, and were therefore, also, on average located further from the cell centre than the H. vulgare chromosomes. Within the parental genomes, the only exception from a random distribution of the chromosomes was that the two satellited chromosomes of H. vulgare were located closer to each other and to the cell centre than can be attributed to chance. This association was most clearly expressed for the telomeres of the chromosome arms carrying the satellites. The data suggest that the parental chromosome complements constitute separate units. This was supported by the observation that five cells had their genomes arranged side-by-side.

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“…Note that this definition of alternating paths or cycles differs from the usual one, which is with respect to only two colors. Besides a number of applications in graph theory and algorithms, the concept of alternating paths and cycles, appears in various other fields: Genetics [7][8][9], social sciences [6], etc. A good resource on alternating paths and cycles is the survey paper [2] by Bang-Jensen and Gutin.…”

Section: Introductionmentioning

confidence: 99%