منابع مشابه
Almost all Regular Graphs are Hamiltonian
In a previous paper the authors showed that almost all labelled cubic graphs are hamiltonian. In the present paper, this result is used to show that almost all r-regular graphs are hamiltonian for any fixed r ≥ 3, by an analysis of the distribution of 1-factors in random regular graphs. Moreover, almost all such graphs are r-edge-colourable if they have an even number of vertices. Similarly, al...
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It is an open problem whether Yao-Yao graphs YYk (also known as sparse-Yao graphs) are all spanners when the integer parameter k is large enough. In this paper we show that, for any integer k ≥ 42, the Yao-Yao graph YY2k is a tk-spanner, with stretch factor tk = 6.03 +O(k −1) when k tends to infinity. Our result generalizes the best known result which asserts that all YY6k are spanners for k ≥ ...
متن کاملAlmost All k-Colorable Graphs are Easy to Color
We describe a simple and eecient heuristic algorithm for the graph coloring problem and show that for all k 1, it nds an optimal coloring for almost all k-colorable graphs. We also show that an algorithm proposed by Br elaz and justiied on experimental grounds optimally colors almost all k-colorable graphs. EEcient implementations of both algorithms are given. The rst one runs in O(n+m log k) t...
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We study the distribution of palindromic numbers (with respect to a fixed base g ≥ 2) over certain congruence classes, and we derive a nontrivial upper bound for the number of prime palindromes n ≤ x as x → ∞. Our results show that almost all palindromes in a given base are composite. ∗MSC Numbers: 11A63, 11L07, 11N69 †Corresponding author 1
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Two variations of set intersection representation are investigated and upper and lower bounds on the minimum number of labels with which a graph may be represented are found which hold for almost all graphs. Speciically, if k (G) is deened to be the minimum number of labels with which G may be represented using the rule that two vertices are adjacent if and only if they share at least k labels,...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1984
ISSN: 0012-365X
DOI: 10.1016/0012-365x(84)90035-9