Claws for thought

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Claws for thought

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Genus Distributions for Iterated Claws

We derive a recursion for the genus distributions of the graphs obtained by iteratively attaching a claw to the dipole D3. The minimum genus of the graphs in this sequence grows arbitrarily large. The families of graphs whose genus distributions have been calculated previously are either planar or almost planar, or they can be obtained by iterative single-vertex or single-edge amalgamation of s...

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Forbidden Pairs for Vertex-Disjoint Claws

Let k ≥ 4, and let H1, H2 be connected graphs with |V (Hi)| ≥ 3 for i = 1, 2. A graph G is said to be {H1, . . . , Hl}-free if none of H1, . . . , Hl is an induced subgraph of G. We prove that if there exists a positive integer n0 such that every {H1, H2}-free graph G with |V (G)| ≥ n0 and δ(G) ≥ 3 contains k vertex-disjoint claws, then {H1, H2} ∩ {K1,t | t ≥ 2} = ∅. Also, we prove that every K...

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Distance-regular graphs without 4-claws

We determine the distance-regular graphs with diameter at least 3 and c2 ≥ 2 but without induced K1,4-subgraphs.

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Concealed weapons: erectile claws in African frogs.

Vertebrate claws are used in a variety of important behaviours and are typically composed of a keratinous sheath overlying the terminal phalanx of a digit. Keratinous claws, however, are rare in living amphibians; their microstructure and other features indicate that they probably originated independently from those in amniotes. Here we show that certain African frogs have a different type of c...

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ژورنال

عنوان ژورنال: Current Biology

سال: 2007

ISSN: 0960-9822

DOI: 10.1016/j.cub.2007.11.042