Saturation Number for Linear Forest 2P3 ∪ tP2

2019 ◽  
Vol 24 (4) ◽  
pp. 283-289
Author(s):  
Min Liu ◽  
Zhiquan Hu
2020 ◽  
Vol 12 (03) ◽  
pp. 2050036
Author(s):  
Dongqin Cheng

The folded hypercube is an important interconnection network for multiprocessor systems. Let [Formula: see text] with [Formula: see text] denote an [Formula: see text]-dimensional folded hypercube. For a given fault-free edge set [Formula: see text] with [Formula: see text] and a faulty edge set [Formula: see text] with [Formula: see text], in this paper we prove that [Formula: see text] contains a fault-free Hamiltonian cycle including each edge of [Formula: see text] if and only if the subgraph induced by [Formula: see text] is linear forest. Furthermore, we give the definitions of the distance among three vertex-disjoint edges and the distance between a vertex and a vertex set. For three vertex-disjoint edges [Formula: see text], the distance among them is denoted by [Formula: see text]. For a vertex [Formula: see text] and a vertex set [Formula: see text], the distance between [Formula: see text] and [Formula: see text] is denoted by [Formula: see text].


2019 ◽  
Vol 342 (4) ◽  
pp. 943-950
Author(s):  
François Dross ◽  
Mickael Montassier ◽  
Alexandre Pinlou

2002 ◽  
Vol 8 (2) ◽  
pp. 82 ◽  
Author(s):  
Michael A. MacDonald ◽  
Robert J. Taylor ◽  
Steven G. Candy

In Tasmania, a system of 100 m wide strips of native forest, referred to as wildlife habitat strips, is retained within production forest, including plantations. Thirty-nine points in 18 wildlife habitat strips within both eucalypt and pine plantations (which were not differentiated for the purposes of the present study) were paired with points in nearby extensive native forest and surveyed for birds. At non-riparian sites (upper slopes and ridges), bird species richness and total abundance were both significantly lower in habitat strips than in controls. This difference is quantitative rather than qualitative, as ordination did not distinguish strip sites and controls, and no species were obviously absent from habitat strips. Riparian zones showed no significant difference in species richness and total abundance between habitat strips and controls. Species richness and total abundance relative to controls increased as wildlife habitat strip length increased over the measured range (0.4-2.1 km). It is thought that this may be because birds perceive strips as linear forest patches rather than corridors, so that there may be a habitat area effect. Other strip characteristics such as width and plantation age were not significant in riparian areas, but may be important on upper slopes and ridges, and the former will affect strip area. Wildlife habitat strips appear to be a valuable component of a conservation programme for birds in production forests in Tasmania.


2018 ◽  
Vol 341 (4) ◽  
pp. 1166-1170
Author(s):  
A. Mohammadian ◽  
B. Tayfeh-Rezaie

2012 ◽  
Vol 15 ◽  
pp. 56-62 ◽  
Author(s):  
Jean-François Couturier ◽  
Petr A. Golovach ◽  
Dieter Kratsch ◽  
Daniël Paulusma

2009 ◽  
Vol 36 (6) ◽  
pp. 488 ◽  
Author(s):  
Susan M. Carthew ◽  
Briony Horner ◽  
Katherine M. W. Jones

Linear forest clearings created by utility corridors have the potential to fragment landscapes, create edge effects and isolate populations of plants and animals. Here, we investigated the impact of utility corridors on small terrestrial fauna inhabiting Nangwarry Native Forest Reserve, south of Penola in south-eastern South Australia. Twelve sites straddling linear clearings of two widths (1.5 and 4.2 m) were surveyed over 2 years with 53 traps arranged as five transects at each site. This resulted in a total of 933 captures of 18 vertebrate species, including four amphibians, eight reptiles and six mammals. Propensity for capture near edges v. interiors, distances moved between recaptures and willingness to cross linear clearings varied among species, and was not related to taxa groups. For example, the small skink Bassiana duperreyi was extremely mobile and crossed tracks regularly. At the other extreme, the frog Neobatrachus pictus was more likely to be caught on interior transects and was never recorded moving between captures. The small dasyurid Antechinus flavipes was the most regularly caught species, and made both short- (<50 m) and long-distance (>1500 m) movements, with longer moves made by dispersing juveniles. Movements by this species often involved clearing crossings, although these were more likely when time between recaptures was longer, particularly for females. However, the overall rate of crossings for this species was not different from that expected if movements were random. In conclusion, the relatively narrow utility corridors studied here did not appear to affect the mobility of the majority of vertebrates significantly, with approximately half of the 85 movements recorded being of animals crossing a clearing, and no significant difference between the proportion crossing the wider (4.2 m) and the narrower (1.5 m) clearings. The present study is one of only a handful investigating movement patterns in reptiles and amphibians, particularly in relation to disturbances. However, sample sizes were small for some species, and future work should focus on those species that look to be either particularly mobile or sedentary, and encompass responses to the wider (up to 15 m) permanent tracks in the region.


2017 ◽  
Vol 4 (2) ◽  
Author(s):  
Ridayati Ridayati

The number of students who coming from the outside of Yogyakarta is the main cause of the rapid growth. Hence, it’s impacted to transportation sector. In addition, one of the densenly traffic areas in Yogya phone’s Intersection. The purposes of this paper are to analize and evaluate the level of service provided by jogja phone’s intersection, and also identify the effect of saturation degree to number of stop. Based on traffic analysis cycle time, the service level to the traffic flow at the Jogja phone’s intersection at the present time is very low, that is F category. After the rearrangement process using MKJI 1997, it obtained a B level of service. In addition, the results of the analysis using SPSS 15, there is no significant effect between the degrees of saturation to the numbers of stop. Keywords: Degree of Saturation, Number of Stop, dan Regression


10.37236/9302 ◽  
2020 ◽  
Vol 27 (4) ◽  
Author(s):  
Lele Liu ◽  
Changxiang He ◽  
Liying Kang

Let $G$ be a graph. We say an $r$-uniform hypergraph $H$ is a Berge-$G$ if there exists a bijection $\phi: E(G)\to E(H)$ such that $e\subseteq\phi(e)$ for each $e\in E(G)$. Given a family of $r$-uniform hypergraphs $\mathcal{F}$ and an $r$-uniform hypergraph $H$, a spanning sub-hypergraph $H'$ of $H$ is $\mathcal{F}$-saturated in $H$ if $H'$ is $\mathcal{F}$-free, but adding any edge in $E(H)\backslash E(H')$ to $H'$ creates a copy of some $F\in\mathcal{F}$. The saturation number of $\mathcal{F}$ is the minimum number of edges in an $\mathcal{F}$-saturated spanning sub-hypergraph of $H$. In this paper, we asymptotically determine the saturation number of Berge stars in random $r$-uniform hypergraphs.


Author(s):  
Halina Bielak ◽  
Kinga Dąbrowska

The Ramsey number \(R(G, H)\) for a pair of graphs \(G\) and \(H\) is defined as the smallest integer \(n\) such that, for any graph \(F\) on \(n\) vertices, either \(F\) contains \(G\) or \(\overline{F}\) contains \(H\) as a subgraph, where \(\overline{F}\) denotes the complement of \(F\). We study Ramsey numbers for some subgraphs of generalized wheels versus cycles and paths and determine these numbers for some cases. We extend many known results studied in [5, 14, 18, 19, 20]. In particular we count the numbers \(R(K_1+L_n, P_m)\) and \(R(K_1+L_n, C_m)\) for some integers \(m\), \(n\), where \(L_n\) is a linear forest of order \(n\) with at least one edge.


2010 ◽  
Vol 02 (04) ◽  
pp. 437-444 ◽  
Author(s):  
I. WAYAN SUDARSANA ◽  
HILDA ASSIYATUN ◽  
ADIWIJAYA ◽  
SELVY MUSDALIFAH

Let H be a graph with the chromatic number h and the chromatic surplus s. A connected graph G of order n is called H-good if R(G, H) = (n - 1)(h - 1) + s. In this paper, we show that Pn is 2Km-good for n ≥ 3. Furthermore, we obtain the Ramsey number R(L, 2Km), where L is a linear forest. Moreover, we also give the Ramsey number R(L, Hm) which is an extension for R(kPn, Hm) proposed by Ali et al. [1], where Hm is a cocktail party graph on 2m vertices.


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