Form Subdivisions
نویسندگان
چکیده
منابع مشابه
Totally odd subdivisions and parity subdivisions: Structures and Coloring
A totally odd H-subdivision means a subdivision of a graph H in which each edge of H corresponds to a path of odd length. Thus this concept is a generalization of a subdivision of H. In this paper, we give a structure theorem for graphs without a fixed graph H as a totally odd subdivision. Namely, every graph with no totally odd H-subdivision has a tree-decomposition such that each piece is eit...
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A fundamental theorem in graph theory states that any 3-connected graph contains a subdivision of K4. As a generalization, we ask for the minimum number of K4-subdivisions that are contained in every 3connected graph on n vertices. We prove that there are Ω(n) such K4subdivisions and show that the order of this bound is tight for infinitely many graphs. We further prove that the computational c...
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Let A be a (small) category. For example, monoids (sets with associative and unital products) can be identified with categories with a single object. Analogously, posets can be identified with those categories A with at most one arrow between any two objects by defining x ≤ y if there is an arrow x −→ y between the objects x and y of A . In particular, we write [n] for the poset {0 < 1 · · · < ...
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Let k be an integer. A graph G is k-arrangeable (concept introduced by Chen and Schelp) if the vertices of G can be numbered v1, v2, . . . , vn in such a way that for every integer i with 1 ≤ i ≤ n, at most k vertices among {v1, v2, . . . , vi} have a neighbor v ∈ {vi+1, vi+2, . . . , vn} that is adjacent to vi. We prove that for every integer p ≥ 1, if a graph G is not p arrangeable, then it c...
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ژورنال
عنوان ژورنال: Library Resources & Technical Services
سال: 2001
ISSN: 0024-2527,2159-9610
DOI: 10.5860/lrts.45n4.187