A (P3-free, K3-free)-colouring of a graph G = (V, E) is a partition of V = A ∪ B such that G[A] is P3-free and G[B] is K3-free. This problem is known to be NP-complete even when restricted to planar graphs and perfect graphs. In this paper, we provide a finite list of 17 forbidden induced subgraphs for cographs with a (P3-free, K3-free)colouring. This yields a linear time recognition algorithm.

AgraphG is free (a, b)-choosable if for any vertex v with b colors assigned and for any list of colors of size a associated with each vertex u = v, the coloring can be completed by choosing for u a subset of b colors such that adjacent vertices are colored with disjoint color sets. In this note, a necessary and sufficient condition for a cycle to be free (a, b)-choosable is given. As a corollar...

cellulose sulfuric acid was used as an efficient biopolymer-based catalyst for the synthesis of tetrahydropyrimido[4,5-b]quinoline-2,4,6-triones and hexahydro-2h-pyrazolo[5,4-b]quinoline-6-ones via three component reaction of aldehyde, 5,5-dimethyl-1,3-cyclohexadione and 6-amino-1,3-dimethyluracil or 5-amino-3-methyl-1-phenypyrazole under solvent-free conditions at 90 oc. the major advantages o...

response of tea plants to b deficiency was studied in hydroponic medium under environmentally controlled conditions. plants height, number of leaves and dry matter production of shoot and root were significantly decreased by b deficiency. concentration of chlorophyll, carotenoids, anthocyanins and flavonoids was not affected by b deficiency in the young leaf, while a significant reduction of ch...

In this paper, we introduce a new normal form for context-free grammars, called reversible context-free grammars, for the problem of learning context-free grammars from positive-only examples. A context-free grammar G = (N, Z, P, S) is said to be reversible if (1) A + G( and B -+ a in P implies A = B and (2) A -+ a@ and A --f aCfl in P implies B = C. We show that the class of reversible context...