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Discrete Mathematics: Special Issue Combinatorics 2010: International Conference dedicated to the memory of Adriano Barlotti
No full textPerfect Octagon Quadrangle Systems with upper C(4)-systems and a large spectrum
No full textAn octagon quadrangle is the graph consisting of an 8-cycle (x1,x2,...,x8) with two additional chords: the edges {x1,x4} and {x5,x8}. An octagon quadrangle system of order v and index λ (OQS) is a pair (X,H), where X is a finite set of v vertices and H is a collection of edge disjoint octagon quadrangles (called blocks) which partition the edge set of $\lambda λKv defined on X. An octagon quadrangle system Σ=(X,H) of order v and index λ is said to be upper C4-perfect if the collection of all of the upper 4-cycles contained in the octagon quadrangles form a μ-fold 4-cycle system of order v; it is said to be upper strongly perfect if the collection of all of the upper 4-cycles contained in the octagon quadrangles form a μ-fold 4-cycle system of order v and also the collection of all of the outside 8-cycles contained in the octagon quadrangles form a ρ-fold 8-cycle system of order v. In this paper, the authors determine the spectrum for these systems, in the case that it is the largest possible
Perfect octagon quadrangle systems
No full textAn octagon quadrangle is the graph consisting of an 8-cycle (x1,...,x8) with two additional chords: the edges {x1,x4},{x1,x4} and {x5,x8}. An octagon quadrangle system (OQS) of order v and index λ is a pair (X,B), where X is a finite set of v vertices and B is a collection of edge disjoint octagon quadrangles, which partitions the edge set of λK(v) defined on X. An OQS Σ=(X,B) of order v and index λ is strongly perfect if the collection of all the inside 4-cycles contained in the octagon quadrangles form a μ-fold 4-cycle system of order v, and the collection of all the outside 8-cycle quadrangles contained in the octagon quadrangles form a ρ-fold 8-cycle system of order v. More generally, C4-perfect OQSs and C8-perfect OQSs are also defined. In this paper, following the ideas of polygon systems introduced by L. Gionfriddo in her papers [Bull. Inst. Combin. Appl. 48 (2006), 73-81; MR2259705; Discrete Math. 308 (2008), no. 2-3, 231-241; MR2378021 (2008k:05167); Australas. J. Combin. 36 (2006), 167-176; MR2262617 (2007e:05025); Discrete Math. 309 (2009), no. 2, 505-512; MR2478727 (2010f:05122)], we determine completely the spectrum of strongly perfect OQSs, C4-perfect OQSs and C8-perfect OQSs, having the minimum possible value for their indices
Work of breathing and mechanical properties of the respiratory system in a rat model of oleic acid induced lung injury
No full textLower and upper chromatic numbers for BSTSs(2^h-1)
No full textIn [Discrete Math. 174, (1997) 247-259] an infinite class of STSs(2^h-1) was found with the upper chromatic number . We prove that in this class, for all STSs(2^h-1) with h <10, the lower chromatic number coincides with the upper chromatic number, i.e. ; moreover, there exists an infinite sub-class of STSs with for any value of h
Lower and upper chromatic numbers for BSTSs(2h - 1)
Get PDFIn [Discrete Math. 174, (1997) 247-259] an infinite class of STSs(2h - 1) was found with the upper chromatic number not(χ)=h.
We prove that in this class, for all STSs(2h - 1) with h<10, the lower chromatic number coincides with the upper chromatic number, i.e. χ=not(χ)=h and moreover, there exists a infinite sub-class of STSs with χ=not(χ)=h for any value of h
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