On the eulericity of a graph

Matthews, Keith R.

doi:10.1002/jgt.3190020207

Cited by 20 publications

(11 citation statements)

References 5 publications

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“…We excluded studies that did not report both isotopes or did not include soil water. Stable isotope data reported in the original papers were extracted either directly from tables or the text or through the data extraction tool Graph Data Extractor (Matthews, ) or obtained from digital repositories. The database includes isotope data from soil water ( n = 5,328) and xylem water ( n = 2,579) from 77 study sites (some papers reported data from more than one site, so the number of study sites is larger than the numbers of screened papers) belonging to four different climate zones of the world, according to Köppen classification (Peel, Finlayson, & McMahon, ; Figure ; Table S1).…”

Section: Methodsmentioning

confidence: 99%

Depth distribution of soil water sourced by plants at the global scale: A new direct inference approach

et al. 2020

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The depth distribution of soil water contributions to plant water uptake is poorly known. Here we evaluate the main water sources used by plants at the global scale and the effect of climate and plant groups on water uptake variability and depth distribution. The global meta‐analysis is based on isotope data (δ2H and δ18O) extracted from 65 peer‐reviewed papers published between 1990 and 2017. We applied a new direct inference method to quantify the overlap between xylem water and soil water sources used by plants. The median overlap between xylem water and soil water at different depths varied between 28% and 100%, but they were generally >50%. The shallow (0‐10 cm) soil water overlap with xylem water was largest in cold regions (100% ± 0%) and lowest at tropical sites (about 28%). Conversely, the median overlap between xylem water and deep soil water was largest in the arid and the tropical zones (>75%) and much smaller in the temperate and cold zones. Our results suggest that the isotopic composition of xylem water reflects mostly the signature of shallow soil water (<30 cm) in the cold and the temperate zones, whereas in the arid and the tropical zones, plants appear to exploit water in deeper soil layers. Our novel, simple statistically‐based direct inference method performed well in determining these differences in water sources, and can be applied more widely to isotope‐based plant water uptake studies.

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Section: Methodsmentioning

confidence: 99%

Depth distribution of soil water sourced by plants at the global scale: A new direct inference approach

et al. 2020

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“…Such decompositions represent a counterpart to decompositions into even subgraphs, which were mainly used while proving various flow problems (see e.g. [6,9]). Historically speaking, as a topic in graph theory, decomposing into subgraphs of a particular kind started with the paper of Erdös et al [2].…”

Section: Odd Edge-colorings and Odd Chromatic Indexmentioning

confidence: 99%

Odd edge-colorability of subcubic graphs

2016

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An edge-coloring of a graph G is said to be odd if for each vertex v of G and each color c, the vertex v either uses the color c an odd number of times or does not use it at all. The minimum number of colors needed for an odd edge-coloring of G is the odd chromatic index χ o (G). These notions were introduced by Pyber in [7], who showed that 4 colors suffice for an odd edge-coloring of any simple graph. In this paper, we consider loopless subcubic graphs, and give a complete characterization in terms of the value of their odd chromatic index.

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“…Tutte [19,20] and Matthews [17] conjectured that if a 2-edge-connected graph G has no subgraph contractible to the Petersen graph, then G has a 3-colorable double cycle cover (i.e., a collection of three even subgraphs such that each edge of G lies in exactly two of them). We showed before (see [5 or 6]) that any supereulerian graph has a 3-colorable double cycle cover.…”

Section: O(g)=[odd-degree Vertices Of G]mentioning

confidence: 99%