On graphs presentable by pattern-avoiding words
نویسندگان
چکیده
منابع مشابه
Representing Graphs via Pattern Avoiding Words
Abstract The notion of a word-representable graph has been studied in a series of papers in the literature. A graph G = (V,E) is word-representable if there exists a word w over the alphabet V such that letters x and y alternate in w if and only if xy is an edge in E. If V = {1, . . . , n}, this is equivalent to saying that G is wordrepresentable if for all x, y ∈ {1, . . . , n}, xy ∈ E if and ...
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Abstract. A word w = w1w2 · · ·wn is alternating if either w1 < w2 > w3 < w4 > · · · (when the word is up-down) or w1 > w2 < w3 > w4 < · · · (when the word is down-up). In this paper, we initiate the study of (pattern-avoiding) alternating words. We enumerate up-down (equivalently, down-up) words via finding a bijection with order ideals of a certain poset. Further, we show that the number of 1...
متن کاملRepresenting Graphs via Pattern Avoiding
The notion of a word-representable graph has been studied in a series of papers in the literature. A graph G = (V,E) is word-representable if there exists a word w over the alphabet V such that letters x and y alternate in w if and only if xy is an edge in E. If V = {1, . . . , n}, this is equivalent to saying that G is word-representable if for all x, y ∈ {1, . . . , n}, xy ∈ E if and only if ...
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In this paper we study the enumeration and the construction, according to the number of ones, of particular binary words avoiding the fixed pattern p( j, i) = 1 j0i, 0 < i < j. The growth of such words can be described by particular jumping and marked succession rules. This approach enables us to obtain an algorithm which constructs all binary words having a fixed number of ones and then kills ...
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In this paper we study the enumeration and the construction of particular binary words avoiding the pattern 10. By means of the theory of Riordan arrays, we solve the enumeration problem and we give a particular succession rule, called jumping and marked succession rule, which describes the growth of such words according to their number of ones. Moreover, the problem of associating a word to a ...
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ژورنال
عنوان ژورنال: Discussiones Mathematicae Graph Theory
سال: 2019
ISSN: 1234-3099,2083-5892
DOI: 10.7151/dmgt.2128