Independent and monochromatic absorbent sets in infinite digraphs
نویسندگان
چکیده
منابع مشابه
Monochromatic paths and monochromatic sets of arcs in quasi-transitive digraphs
Let D be a digraph, V (D) and A(D) will denote the sets of vertices and arcs of D, respectively. We call the digraph D an m-coloured digraph if each arc of D is coloured by an element of {1, 2, . . . , m} where m ≥ 1. A directed path is called monochromatic if all of its arcs are coloured alike. A set N of vertices of D is called a kernel by monochromatic paths if there is no monochromatic path...
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We call the digraph D an m-coloured digraph if the arcs of D are coloured with m colours. A directed path is called monochromatic if all of its arcs are coloured alike. A set N of vertices of D is called a kernel by monochromatic paths if for every pair of vertices of N there is no monochromatic path between them and for every vertex v / ∈ N there is a monochromatic path from v to N . We denote...
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In this paper, we consider the following problem due to Erdős: for each m ∈ N, is there a (least) positive integer f(m) so that every finite mcolored tournament contains an absorbent set S by monochromatic directed paths of f(m) vertices? In particular, is f(3) = 3? We prove several bounds for absorbent sets of m-colored tournaments under certain conditions on the number of colors of the arcs i...
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متن کاملKernels in monochromatic path digraphs
We call the digraphD anm-coloured digraph if its arcs are coloured withm colours. A directed path (or a directed cycle) is called monochromatic if all of its arcs are coloured alike. Let D be an m-coloured digraph. A set N ⊆ V (D) is said to be a kernel by monochromatic paths if it satisfies the following two conditions: (i) for every pair of different vertices u, v ∈ N there is no monochromati...
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ژورنال
عنوان ژورنال: AKCE International Journal of Graphs and Combinatorics
سال: 2015
ISSN: 0972-8600,2543-3474
DOI: 10.1016/j.akcej.2015.11.005