in this paper we define the removable cycle that, if $im$ is a class of graphs, $gin im$, the cycle $c$ in $g$ is called removable if $g-e(c)in im$. the removable cycles in eulerian graphs have been studied. we characterize eulerian graphs which contain two edge-disjoint removable cycles, and the necessary and sufficient conditions for eulerian graph to have removable cycles h...

In this paper we study simple families of clustered graphs that are highly non connected. We start by studying 3-cluster cycles, that are clustered graphs such that the underlying graph is a simple cycle and there are three clusters all at the same level. We show that in this case testing the c-planarity can be done efficiently and give an efficient drawing algorithm. Also, we characterize 3-cl...

A Hamilton circle in an infinite graph is a homeomorphic copy of the unit circle S1 that contains all vertices and all ends precisely once. We prove that every connected, locally connected, locally finite, claw-free graph has such a Hamilton circle, extending a result of Oberly and Sumner to infinite graphs. Furthermore, we show that such graphs are Hamilton-connected if and only if they are 3-...

Very recently, Bialostocki et al. proposed the following conjecture. Let r, s be two nonnegative integers and let G = (V (G), E(G)) be a graph with |V (G)| ≥ 3r + 4s and minimum degree δ(G) ≥ 2r + 3s. Then G contains a collection of r cycles and s chorded cycles, all vertex-disjoint. We prove that this conjecture is true.

this paper investigates the dynamics and stability properties of a discrete-time lotka-volterra type system. we first analyze stability of the fixed points and the existence of local bifurcations. our analysis shows the presence of rich variety of local bifurcations, namely, stable fixed points; in which population numbers remain constant, periodic cycles; in which population numbers oscillate amo...

routinely, a bolus of 5.000-10.000 iu human chorionic gonadotropin (hcg) is usedfor the final follicular maturation and ovulation as a standard method. hcg has thesame effect of luteinizing hormone (lh) with long half-life. it has the longlutheotrophic effect which increases the risk of ovarian hyper stimulation syndrome(ohss). recently, gonadotropin-releasing hormone agonist (gnrh-a) trigger h...