For a class V of graphs, denote by a(@?) the least value of m so that for some graph II on m vertices, every GE Q occurs as a subgraph of U. In this note we obtain rather sharp bounds on u(q) when Q is the class of caterpillars on n vertices, i.e., tree with property that the vertices of degree exceeding one induce a path. Recently several of the authors have investigated graphs U(g) which are ...

Accidental poisoning with caterpillars has become increasingly frequent in southern Brazil, partly due to deforestation and elimination of natural predators [1]. Caterpillars are the larval stage of moths and butterflies and are found worldwide [2]. Accidental contact with caterpillar’s bristles induces allergic and toxic signs and symptoms that range from mild cutaneous reaction to severe syst...

A first analysis of caterpillars of Tineidae and their cases preserved in Eocene Baltic Amber is presented, and an ecological interpretation based on comparisons with extant Tineidae is given. Several informative syninclusions (e.g., mammal hairs, Psocoptera) of two of the cases suggest that the caterpillars of some Tineidae in the Baltic Amber forest occupied comparable ecological niches as th...

Let m≥1 be an integer and G a graph with m edges. We say that has antimagic orientation if D bijection τ:A(D)→{1,…,m} such no two vertices in have the same vertex-sum under τ, where of vertex v τ is sum labels all arcs entering minus leaving v. Hefetz et al. (2010) conjectured every connected admits orientation. The conjecture was confirmed for certain classes graphs as regular graphs, minimum ...

<p style="text-align: justify;">A caterpillar is a tree obtained from path by attaching pendant vertices. The number of caterpillars size <em>n</em> well-known result. In this work extend result exploring the together with cardinalities stable sets and diameter. Three closed formulas are presented, giving with: (i) smaller set cardinality <em>k</em>, (ii) diameter ...

possible to estimate preindustrial CC14 levels accurately from measurements in slowly renewed deep waters (1). In contrast, loss of CH3CC13 would be considerable even in cold waters over a period of only 40 years (that is, since CH3CC13 was introduced into the environment), and it has an input function that is not dramatically different in nature from those of F-li and F-12 (1). We thus reitera...

Let T be a tree such that all its vertices of degree more than two lie on one path; that is, T is a caterpillar subdivision. We prove that there exists > 0 such that for every graph G with |V (G)| ≥ 2 not containing T as an induced subgraph, either some vertex has at least |V (G)| neighbours, or there are two disjoint sets of vertices A,B, both of cardinality at least |V (G)|, where there is no...