# Download Combinatorial Mathematics III: Proceedings of the Third by V. G. Cerf, D. D. Cowan, R. C. Mullin, R. G. Stanton PDF By V. G. Cerf, D. D. Cowan, R. C. Mullin, R. G. Stanton (auth.), Dr. Anne Penfold Street, Dr. Walter Denis Wallis (eds.)

Read or Download Combinatorial Mathematics III: Proceedings of the Third Australian Conference Held at the University of Queensland, 16–18 May, 1974 PDF

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Extra resources for Combinatorial Mathematics III: Proceedings of the Third Australian Conference Held at the University of Queensland, 16–18 May, 1974

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It appears difficult to obtain a s a t i s f a c t o r y characterization. It has been shown by J. Horton  that if a cyclic sequence of edges in w h i d h each edge appears twice is that e n c o u n t e r e d on a left-right path of plane graph Corollary. ) be the number of paths of a 4-regular plane that always violate trated in Figure is unique the component-defining requirement 10, and that contain each edge exactly is odd if and only if H once. illus- Then k has exactly one component. (The r e a d e r is r e f e r r e d to [S] for a c o r r e s p o n d e n c e between such paths and spanning trees of Corollary.

N = 28) are H a m i l t o n i a n However, is a n o n - H a m i l t o n i a n example for the M(28,3). 23 I Figure 2 26A 14 (from 18) 8 12 3, 10 i\ l 5 Fisure 11 26B (from 20A) 24 14 10 8 ~4 2 Figure 26C 12 (from 20B) 11 6 5 1 13 Figure 14 26D (from 22A) v Do o~ ~rj v t~ r~ M o~ ° ~ 26 13 14 10 /1 2 Figure 1 26G (from 23C) 10 13 12 7 1 Figure 26H (from 25A) 27 REFERENCES LI] V. G. Cerf, D. D. Cowan, R. C. Mullin, Topological R. G. Stanton, Design Considerations in Computer Communications Networks in Computer Communication Networks, ed.

2. N E C E S S A R Y CONDITIONS FOR THE EXISTENCE OF BALANCED W E I G H I N G MATRICES Since a BW(v,k) implies the existence of a (v,k,l) configuration, the following conditions are known to be necessary: (i) if v is even then (k-l) must be a perfect square; 29 (ii) if v is odd then the equation x 2 = (k-l)y 2 + (-1) (v-1)/2 It is also have (See [7, trivial (iii) Further must a solution that it is s h o w n for a in for a W(v,k) k (v) if v is odd, then (v-k) 2 - (v-k) shown parameters p It was shown any p r o j e c t i v e of a w e i g h i n g incidence matrix in PG(m,n) where matrix of the signed if b o t h m and construction it is shown a It is n o t e d matrices true part incidence k must is s t r o n g e r is a s o l u t i o n for that k-l is not of of not than (1); (i) but implies matrix k (ii) the is has a divisible of the to as certain signing).