Cycles in Graphs by B. R. Alspach

By B. R. Alspach

This quantity bargains with a number of difficulties related to cycles in graphs and circuits in digraphs. major researchers during this zone current the following three survey papers and forty two papers containing new effects. there's additionally a set of unsolved difficulties.

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5] F. , 9 (19801, 305. D. [71 G. Szekeres, Polyhedral decomposition o f cubic graphs, J. A u s t r a l . Math. Seymur, Sums o f c i r c u i t s , Graph theory and r e l a t e d t o p i c s , ed. A. R. Murty, (Academic P r e s s , New York, 1 9 7 9 ) , 341-355. , 8 (19731, 367-387. V. D. A. I n t h i s p a p e r i t i s shown t h a t e v e r y c o n n e c t e d metac i r c u l a n t g r a p h h a v i n g a n e v e n number o f b l o c k s o f prime c a r d i n a l i t y , o t h e r t h a n t h e sole e x c e p t i o n o f t h e P e t e r s e n graph, h a s a Hamilton cycle.

Szekeres, Polyhedral decomposition o f cubic graphs, J. A u s t r a l . Math. Seymur, Sums o f c i r c u i t s , Graph theory and r e l a t e d t o p i c s , ed. A. R. Murty, (Academic P r e s s , New York, 1 9 7 9 ) , 341-355. , 8 (19731, 367-387. V. D. A. I n t h i s p a p e r i t i s shown t h a t e v e r y c o n n e c t e d metac i r c u l a n t g r a p h h a v i n g a n e v e n number o f b l o c k s o f prime c a r d i n a l i t y , o t h e r t h a n t h e sole e x c e p t i o n o f t h e P e t e r s e n graph, h a s a Hamilton cycle.

S (b-l)a’ Let R) R’ be any permutation of R , and put Hamilton Paths in Cartesian Products (zi : 1 5 i < ab) = (R’, sa’ (zi : 1 5 i < ab) If some m and n n i=l C z z . z . = i=1 + , mx z. C ’ 0 5 m < n < a b , we must have z m , s (b-1)a’ R’) a * . does not list the arcs of a Hamilton path, then for with m Because 49 m E n (mod a) we must have i=l a/n . Then aim. This yields m n m c I: = s i=l i z i=l (zi : 1 c i < ab) i ab-1 z i=l C z i = i=l si, i=l (si : 1 c i < ab) is a Hamilton path.

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