Decompositions into two paths

• Autorzy: Zdzisław Skupień
• Języki publikacji: EN

Abstrakty

EN

It is proved that a connected multigraph G which is the union of two edge-disjoint paths has another decomposition into two paths with the same set, U, of endvertices provided that the multigraph is neither a path nor cycle. Moreover, then the number of such decompositions is proved to be even unless the number is three, which occurs exactly if G is a tree homeomorphic with graph of either symbol + or ⊥. A multigraph on n vertices with exactly two traceable pairs is constructed for each n ≥ 3. The Thomason result on hamiltonian pairs is used and is proved to be sharp.

Słowa kluczowe

EN

graph; multigraph; path decomposition; hamiltonian decomposition; traceable

Kategorie tematyczne

• 05C70: Factorization, matching, partitioning, covering and packing
• 05C35: Extremal problems
• 05C45: Eulerian and Hamiltonian graphs
• 05C38: Paths and cycles

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2005
• Tom: 25
• Numer: 3
• Strony: 325-329

Daty

wydano

2005

otrzymano

2004-03-08

poprawiono

2004-11-02

Twórcy

autor

Zdzisław Skupień

• Faculty of Applied Mathematics, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Kraków, Poland

Bibliografia

• [1] http://listserv.nodak.edu/archives/graphnet.html.
• [2] S. Lin, Computer solutions of the traveling salesman problem, Bell System Tech. J. 44 (1965) 2245-2269.
• [3] Z. Skupień, Sparse hamiltonian 2-decompositions together with numerous Hamilton cycles, submitted.
• [4] N.J.A. Sloane, Hamiltonian cycles in a graph of degree four, J. Combin. Theory 6 (1969) 311-312, doi: 10.1016/S0021-9800(69)80093-1.
• [5] K.W. Smith, Two-path conjecture, in: [1], Feb. 16, 2001.
• [6] A.G. Thomason, Hamiltonian cycles and uniquely edge colourable graphs, in: B. Bollobás, ed., Advances in Graph Theory (Proc. Cambridge Combin. Conf., 1977), Ann. Discrete Math. 3 (1978) (North-Holland, Amsterdam, 1978) pp. 259-268.
• [7] D.B. West, Introduction to Graph Theory (Prentice Hall, Upper Saddle River, NJ, 1996).
• [8] D. West, in: [1], Feb. 20, 2001.

Identyfikatory

DOI

10.7151/dmgt.1285