منابع مشابه
Maximal Nontraceable Graphs with Toughness less than One
A graph G is maximal nontraceable (MNT) if G does not have a hamiltonian path but, for every e ∈ E (
متن کاملCubic 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 کاملLower 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 کاملFurther results on Maximal Nontraceable graphs of smallest size
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متن کاملNontraceable 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...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2008
ISSN: 1077-8926
DOI: 10.37236/742