On the toughness of cycle permutation graphs

Chong-Yun Chao; Shaocen Han

Czechoslovak Mathematical Journal (2001)

  • Volume: 51, Issue: 2, page 239-260
  • ISSN: 0011-4642

Abstract

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Motivated by the conjectures in [11], we introduce the maximal chains of a cycle permutation graph, and we use the properties of maximal chains to establish the upper bounds for the toughness of cycle permutation graphs. Our results confirm two conjectures in [11].

How to cite

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Chao, Chong-Yun, and Han, Shaocen. "On the toughness of cycle permutation graphs." Czechoslovak Mathematical Journal 51.2 (2001): 239-260. <http://eudml.org/doc/30632>.

@article{Chao2001,
abstract = {Motivated by the conjectures in [11], we introduce the maximal chains of a cycle permutation graph, and we use the properties of maximal chains to establish the upper bounds for the toughness of cycle permutation graphs. Our results confirm two conjectures in [11].},
author = {Chao, Chong-Yun, Han, Shaocen},
journal = {Czechoslovak Mathematical Journal},
keywords = {cycle permutation graph; toughness; maximal chain; cycle permutation graph; toughness; maximal chain},
language = {eng},
number = {2},
pages = {239-260},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the toughness of cycle permutation graphs},
url = {http://eudml.org/doc/30632},
volume = {51},
year = {2001},
}

TY - JOUR
AU - Chao, Chong-Yun
AU - Han, Shaocen
TI - On the toughness of cycle permutation graphs
JO - Czechoslovak Mathematical Journal
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 51
IS - 2
SP - 239
EP - 260
AB - Motivated by the conjectures in [11], we introduce the maximal chains of a cycle permutation graph, and we use the properties of maximal chains to establish the upper bounds for the toughness of cycle permutation graphs. Our results confirm two conjectures in [11].
LA - eng
KW - cycle permutation graph; toughness; maximal chain; cycle permutation graph; toughness; maximal chain
UR - http://eudml.org/doc/30632
ER -

References

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  1. Some recent results on long cycles in tough graphs, Graph Theory, Combinatorics, and Applications—Proceedings of the Sixth Quadrennial International Conference on the Theory and Applications of Graphs, Y.  Alavi, G.  Chartrand, O. R. Oellermann, and A. J. Schwenk (eds.), John Wiley & Sons, New York, 1991, pp. 113–121. (1991) MR1170772
  2. Cycles in tough graphs-updating the last four years, Graph Theory, Combinatorics, and Applications—Proceedings of the Seventh Quadrennial International Conference on the Theory and Applications of Graphs, Y.  Alavi and A. J.  Schwenk (eds.), Wiley & Sons, New York, 1995, pp. 19–34. (1995) MR1405796
  3. A note on the toughness of generalized Petersen graphs, J. Math. Res. Exposition 12 (1992), 183–186. (1992) MR1167349
  4. 10.1023/A:1022455216281, Czechoslovak Math. J. 47 (1997), 431–452. (1997) MR1461423DOI10.1023/A:1022455216281
  5. The Petersen graph, Graphs and Applications, F.  Harary and J. S.  Maybee (eds.), John Wiley & Sons, 1982, pp. 69–99. (1982) MR0778399
  6. Tough graphs and hamiltonian circuits, Math. Slovaca 28 (1979), 215–228. (1979) MR0316301
  7. On mapping graphs and permutation graphs, Math. Slovaca 28 (1979), 277–288. (1979) MR0534995
  8. On the toughness of some generalized Petersen graphs, Ars Combin. (1993), 65–88. (1993) Zbl0793.05083MR1246901
  9. 10.1007/BF01858441, Graphs Combin. 12 (1996), 17–22. (1996) Zbl0846.05049MR1381524DOI10.1007/BF01858441
  10. On the vulnerability of permutation graphs of complete and complete bipartite graphs, Ars Combin. 31 (1991), 149–157. (1991) MR1110229
  11. On the vulnerability of cycle permutation graphs, Ars Combin. 29 (1990), 289–296. (1990) MR1046114
  12. 10.1016/S0021-9800(66)80004-2, J.  Combin. Theory 1 (1960), 15–50. (1960) MR0194363DOI10.1016/S0021-9800(66)80004-2

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