We consider the problem of covering a host graph G with several graphs from a fixed template class T . The classical covering number of G with respect to T is the minimum number of template graphs needed to cover the edges of G. We introduce two new parameters: the local and the folded covering number. Each parameter measures how far G is from the template class in a different way. Whereas the ...

The celebrated Erdős-Hajnal conjecture states that for every proper hereditary graph class G there exists a constant ε = ε(G) > 0 such that every graph G ∈ G contains a clique or an independent set of size |V (G)|. Recently, there has been a growing interest in the symmetrized variant of this conjecture, where one additionally requires G to be closed under complementation. We show that any here...

Leaf-tying caterpillars act as ecosystem engineers by building shelters between overlapping leaves, which are inhabited by other arthropods. Leaf-tiers have been observed to leave their ties and create new shelters (and thus additional microhabitats), but the ecological factors affecting shelter fidelity are poorly known. For this study, we explored the effects of resource limitation and occupa...

Wheelchairs are an important means of transportation for the elderly and disabled. However, movement wheelchairs on long curbs stairs is restricted. In this study, a wheelchair climbing was developed based mechanical transmission system that rotates entire driving part through link structure actuator to change speed. The first mode drives caterpillar, second wheels. When flat ground, it uses la...

Let G = ( V , E ) be a simple, undirected and connected graph. A dominating set S is called secure if for each u ∈ \ there exists v such that \{ }) ∪{ } of . If further the vertex unique, then perfect (PSDS). The domination number γ ps minimum cardinality Given graph positive integer k (PSDOM) problem to check whether has PSDS size at most In this paper, we prove PSDOM NP-complete split graphs,...

Some parasites alter the behaviour of their hosts. The larvae of the parasitic wasp Cotesia congregata develop within the body of the caterpillar Manduca sexta During the initial phase of wasp development, the host's behaviour remains unchanged. However, once the wasps begin to scrape their way out of the caterpillar, the caterpillar host stops feeding and moving spontaneously. We found that th...

Caterpillar recently embarked on an ambitious program to radically change how it markets and sells key products of its Building Construction Products division (BCP). The goal was to move from a strict build-toorder strategy, in which customers selected one of millions of possible configurations, to a Lane Strategy in which the majority of their customers would choose machines from just over 100...

<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 ...

Background Thaumetopoea pityocampa Schiff., or pine caterpillar, is a “phenomenal” insect. The term comes from the Greek cámpa (caterpillar), pítys (pine), poieo (does), tháuma (wonders) [1]. When developing larvae, is taking place on the back of the caterpillar pine processionary, a producer apparatus urticating hairs, protectors caterpillars [2]. These hairs of the pine processionary caterpil...