We show that every K4-free graph G with n vertices can be made bipartite by deleting at most n/9 edges. Moreover, the only extremal graph which requires deletion of that many edges is a complete 3-partite graph with parts of size n/3. This proves an old conjecture of P. Erdős.

Rabbit esophageal epithelium, a parakeratinized stratified epithelium, synthesizes as one of its major differentiation products a keratin pair consisting of a basic K4 (59 kDa) and an acidic K13 (41 kDa) keratin. Although immunohistochemical staining data suggest that in esophageal epithelia of some other species these two keratins are suprabasally located, antigenic masking of the epitopes in ...

The current study was carried out at the experimental farm of Rana Sugars Ltd., Buttar Seviyan, Amritsar, Punjab, India, to identify methods improve yield and quality ratoon sugarcane in potassium-deficient soils. treatments comprised two levels irrigation, resulting plants which either received sufficient water (I1) or were water-stressed (I2), four rates potassium (K) application: 0 (K1), 40 ...