Question: Are Caralluma and Parthenocissus both climbing plants?

Context paragraphs:
Caralluma: Caralluma is a genus of flowering plants in the dogbane family, Apocynaceae, consisting of about 120 species.

Darwin from Insectivorous Plants to Worms: Between 1873 and 1882, the life and work of Charles Darwin from "Insectivorous Plants" to "Worms" continued with investigations into carnivorous and climbing plants that had begun with his previous work.  Worries about family illnesses contributed to his interest in Galton's ideas of "hereditary improvement" (which would later be called Eugenics).  He continued to help with the work of Downe parish church and associated village amenities, despite problems with control being seized by a new High Church vicar, and he remained on good terms with the Church's patron, the Revd.  John Brodie Innes.  There was continuing interest in Charles Darwin's views on religion, but he remained reticent.

Berchemia: Berchemia is a genus of plants in the family Rhamnaceae, named after Dutch botanist Berthout van Berchem.  They are climbing plants or small to medium-sized trees that occur in Africa, Asia and the Americas.

Asparagus (genus): Asparagus is a genus of flowering plants in the family Asparagaceae, subfamily Asparagoideae.  It comprises up to 300 species.  Most are evergreen long-lived perennial plants growing from the understory as lianas, bushes or climbing plants.  The best-known species is the edible "Asparagus officinalis", commonly referred to as just "asparagus".  Some other members of the genus, such as "Asparagus densiflorus", are grown as ornamental plants.

Darwin from Orchids to Variation: Between 1860 and 1868, the life and work of Charles Darwin from "Orchids" to "Variation" continued with research and experimentation on evolution, carrying out tedious work to provide evidence of the extent of natural variation enabling artificial selection.  He was repeatedly held up by his illness, and continued to find relaxation and interest in the study of plants.  His studies of insect pollination led to publication of his book "Fertilisation of Orchids" as his first detailed demonstration of the power of natural selection, explaining the complex ecological relationships and making testable predictions.  As his health declined, he lay on his sickbed in a room filled with inventive experiments to trace the movements of climbing plants.

Kennedia: Kennedia is a genus of plants comprising 16 species, all native to Australia.  They are evergreen climbing plants with woody stems.  They usually have trifoliate leaves and pea-type flowers of various colours from pink to dark red and yellow to black.  The genus was named by Étienne Pierre Ventenat after John Kennedy, a partner in the renowned firm of nurserymen, Lee and Kennedy of Hammersmith, London.

Tentacle (botany): In botany, tentacles are glandular hairs on the leaves of some species of insectivorous plants such as "Drosera" (sundews).  Tentacles are different from organs such as the tendrils of climbing plants.

Parthenocissus: Parthenocissus , is a genus of tendril climbing plants in the grape family, Vitaceae.  It contains about 12 species native to the Himalayas, eastern Asia and North America.  Several are grown for ornamental use, notably "P. henryana", "P. quinquefolia" and "P. tricuspidata".

Trellis (architecture): A trellis (treillage) is an architectural structure, usually made from an open framework or lattice of interwoven or intersecting pieces of wood, bamboo or metal that is normally made to support and display climbing plants, especially shrubs.  There are many types of trellis for different places and for different plants, from agricultural types, especially in viticulture, which are covered at vine training systems, to garden uses for climbers such as grapevines, clematis, ivy, and climbing roses or other support based growing plants.  The rose trellis is especially common in Europe and other rose-growing areas, and many climbing rose varieties require a trellis to reach their potential as garden plants.  Some plants will climb and wrap themselves round a trellis without much artificial help being needed while others need training by passing the growing shoots through the trellis and/or tying them to the framework.

Parthenocissus laetevirens: Parthenocissus laetevirens is a climbing plant species in the genus "Parthenocissus" found in China.

Supporting paragraphs: Caralluma Parthenocissus
Answer: no