The celebrated Frieze's result about the independence number of G(n,p) states that it is concentrated in an interval of size o(1/p) for all Cε/n<p=o(1). We show concentration in an interval of size ...o(1/p) for the maximum size (number of vertices) of an induced forest in G(n,p) for all Cε/n<p<1−ε. Presumably, it is the first generalization of Frieze's result to another class of induced subgraphs for such a range of p.
Shifts in rainfall patterns and increasing temperatures associated with climate change are likely to cause widespread forest decline in regions where droughts are predicted to increase in duration ...and severity. One primary cause of productivity loss and plant mortality during drought is hydraulic failure. Drought stress creates trapped gas emboli in the water transport system, which reduces the ability of plants to supply water to leaves for photosynthetic gas exchange and can ultimately result in desiccation and mortality. At present we lack a clear picture of how thresholds to hydraulic failure vary across a broad range of species and environments, despite many individual experiments. Here we draw together published and unpublished data on the vulnerability of the transport system to drought-induced embolism for a large number of woody species, with a view to examining the likely consequences of climate change for forest biomes. We show that 70% of 226 forest species from 81 sites worldwide operate with narrow (,1 megapascal) hydraulic safety margins against injurious levels of drought stress and therefore potentially face long-term reductions in productivity and survival if temperature and aridity increase as predicted for many regions across the globe. Safety margins are largely independent of mean annual precipitation, showing that there is global convergence in the vulnerability of forests to drought, with all forest biomes equally vulnerable to hydraulic failure regardless of their current rainfall environment. These findings provide insight into why drought-induced forest decline is occurring not only in arid regions but also in wet forests not normally considered at drought risk.
Induced and weak induced arboricities Axenovich, Maria; Dörr, Philip; Rollin, Jonathan ...
Discrete mathematics,
February 2019, 2019-02-00, Volume:
342, Issue:
2
Journal Article
Peer reviewed
Open access
We define the induced arboricity of a graph G, denoted by ia(G), as the smallest k such that the edges of G can be covered with k induced forests in G.
For a class F of graphs and a graph parameter ...p, let p(F)=sup{p(G)∣G∈F}. We show that ia(F) is bounded from above by an absolute constant depending only on F, that is ia(F)≠∞ if and only if χ(F∇12)≠∞, where F∇12 is the class of 12-shallow minors of graphs from F andχ is the chromatic number.
As a main contribution of this paper, we provide bounds on ia(F) when F is the class of planar graphs, the class of d-degenerate graphs, or the class of graphs having tree-width at most d. Specifically, we show that if F is the class of planar graphs, then 8≤ia(F)≤10.
In addition, we establish similar results for so-called weak induced arboricities and star arboricities of classes of graphs.
Equitable partition of planar graphs Kim, Ringi; Oum, Sang-il; Zhang, Xin
Discrete mathematics,
June 2021, 2021-06-00, Volume:
344, Issue:
6
Journal Article
Peer reviewed
Open access
An equitablek-partition of a graph G is a collection of induced subgraphs (GV1,GV2,…,GVk) of G such that (V1,V2,…,Vk) is a partition of V(G) and −1≤|Vi|−|Vj|≤1 for all 1≤i<j≤k. We prove that every ...planar graph admits an equitable 2-partition into 3-degenerate graphs, an equitable 3-partition into 2-degenerate graphs, and an equitable 3-partition into two forests and one graph.
A kite is a complete graph on four vertices with one edge removed. It is proved that every planar graph without a kite as subgraph can be partitioned into two induced forests. This resolves a ...conjecture of Raspaud and Wang in 2008.
This study presents a novel method of tornado track identification in forested regions in Europe based on remote sensing data. The method enables an objective estimate (i.e. independent of population ...density and observational networks) of tornado climatology in forested regions. The method is based on the identification of narrow and elongated areas as forest disturbances obtained using Landsat satellite images and Landsat-based Global Forest Change (GFC) data. These areas were subsequently verified with high-resolution satellite images for verification of a tornadic cause of forest damage. Landsat and MODIS satellite images, weather station observations and reanalysis data were additionally involved in order to determine tornado dates. A minimum F-scale tornado intensity was estimated by a Weibull distribution model using information on tornado path lengths and widths. The method is applied to the forested regions of northeast Europe, where 110 tornado tracks were identified between the 2000 and 2014years, 105 of which were previously unreported and discovered for the first time. For some regions, tornado density estimates using the new method is 2–3 times higher than other previously published estimates. The largest number of tornadoes occurred in 2009, and June is the most favourable month for tornado formation (including strong tornadoes and tornado outbreaks). Most identified tornadoes have path length <10km with maximum and mean widths of approximately 200–300m and 100–200m, respectively. A few tornadoes with long and wide paths were found; four of them likely had F3 minimal intensity.
•A novel method for tornado track identification is proposed.•The method allows robust identification of relatively strong tornadoes in forested areas.•The method was implemented for forested regions of northeast Europe for 2000–2014years.•110 tornado tracks were found, 105 of them were reported for the first time.•Estimated tornado density is 2–3 times higher than previously published.
Large Induced Forests in Graphs Shi, Lingsheng; Xu, Hongyu
Journal of graph theory,
August 2017, 2017-08-00, 20170801, Volume:
85, Issue:
4
Journal Article
Peer reviewed
In this article, we prove three theorems. The first is that every connected graph of order n and size m has an induced forest of order at least (8n−2m−2)/9 with equality if and only if such a graph ...is obtained from a tree by expanding every vertex to a clique of order either 4 or 5. This improves the previous lower bound 2n22m+n of Alon–Kahn–Seymour for m≤5n/2, and implies that such a graph has an induced forest of order at least n/2 for m<⌊7n/4⌋. This latter result relates to the conjecture of Albertson and Berman that every planar graph of order n has an induced forest of order at least n/2. The second is that every connected triangle‐free graph of order n and size m has an induced forest of order at least (20n−5m−5)/19. This bound is sharp by the cube and the Wagner graph. It also improves the previous lower bound n−m/4 of Alon–Mubayi–Thomas for m≤4n−20, and implies that such a graph has an induced forest of order at least 5n/8 for m<⌊13n/8⌋. This latter result relates to the conjecture of Akiyama and Watanabe that every bipartite planar graph of order n has an induced forest of order at least 5n/8. The third is that every connected planar graph of order n and size m with girth at least 5 has an induced forest of order at least (8n−2m−2)/7 with equality if and only if such a graph is obtained from a tree by expanding every vertex to one of five specific graphs. This implies that such a graph has an induced forest of order at least 2(n+1)/3, where 7n/10 was conjectured to be the best lower bound by Kowalik, Lužar, and Škrekovski.
An induced forest k-partition of a graph G is a k-partition (V1,V2,…,Vk) of the vertex set of G such that, for each i with 1≤i≤k, the subgraph induced by Vi is a forest. The vertex-arboricity of a ...graph G is the minimum k such that G has an induced forest k-partition. In the literature, it has been shown that every planar graph of diameter 2 has vertex-arboricity at most 2. The family of K5-minor-free graphs is a generalization of the planar graphs. We show in this paper that every K5-minor-free graph of diameter 2 has vertex-arboricity at most 2.
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