Maximal Nontraceable Graphs with Toughness less than One

نویسندگان

  • Frank Bullock
  • Marietjie Frick
  • Joy Singleton
  • Susan A. van Aardt
  • Christina M. Mynhardt
چکیده

A graph G is maximal nontraceable (MNT) if G does not have a hamiltonian path but, for every e ∈ E (

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Cubic maximal nontraceable graphs

We determine a lower bound for the number of edges of a 2-connected maximal nontraceable graph, and present a construction of an infinite family of maximal nontraceable graphs that realize this bound.

متن کامل

Toughness and hamiltonicity in k-trees

We consider toughness conditions that guarantee the existence of a hamiltonian cycle in ktrees, a subclass of the class of chordal graphs. By a result of Chen et al. 18-tough chordal graphs are hamiltonian, and by a result of Bauer et al. there exist nontraceable chordal graphs with toughness arbitrarily close to 4 . It is believed that the best possible value of the toughness guaranteeing hami...

متن کامل

Nontraceable detour graphs

The detour order (of a vertex v) of a graph G is the order of a longest path (beginning at v). The detour sequence of G is a sequence consisting of the detour orders of its vertices. A graph is called a detour graph if its detour sequence is constant. The detour deficiency of a graph G is the difference between the order of G and its detour order. Homogeneously traceable graphs are therefore de...

متن کامل

More Progress on Tough Graphs - The Y2K Report

We now know that not every 2-tough graph is hamiltonian. In fact for every > 0, there exists a (9/4− ) tough nontraceable graph. We continue our quadrennial survey of results that relate the toughness of a graph to its cycle structure.

متن کامل

Lower Bound for the Size of Maximal Nontraceable Graphs

Let g(n) denote the minimum number of edges of a maximal nontraceable graph of order n. Dudek, Katona and Wojda (2003) showed that g(n) ≥ d3n−2 2 e−2 for n ≥ 20 and g(n) ≤ d3n−2 2 e for n ≥ 54 as well as for n ∈ I = {22, 23, 30, 31, 38, 39, 40, 41, 42, 43, 46, 47, 48, 49, 50, 51}. We show that g(n) = d3n−2 2 e for n ≥ 54 as well as for n ∈ I ∪ {12, 13} and we determine g(n) for n ≤ 9.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Electr. J. Comb.

دوره 15  شماره 

صفحات  -

تاریخ انتشار 2008