Square-Free Graphs with No Six-Vertex Induced Path
نویسندگان
چکیده
منابع مشابه
Triangle-free graphs with no six-vertex induced path
The graphs with no five-vertex induced path are still not understood. But in the triangle-free case, we can do this and one better; we give an explicit construction for all triangle-free graphs with no six-vertex induced path. Here are two examples: the 16-vertex Clebsch graph, and the graph obtained from a complete bipartite graph by subdividing a perfect matching. We show that every connected...
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We prove that a graph G contains no induced 5-vertex path and no induced complement of a 5-vertex path if and only if G is obtained from 5-cycles and split graphs by repeatedly applying the following operations: substitution, split unification, and split unification in the complement, where split unification is a new class-preserving operation introduced here. ∗Princeton University, Princeton, ...
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In this paper, we give a polynomial time algorithm which determines if a given triangle-free graph with no induced seven-vertex path is 3-colorable, and gives an explicit coloring if one exists.
متن کاملOn Square-free Vertex Colorings of Graphs
A sequence of symbols a1, a2 . . . is called square-free if it does not contain a subsequence of consecutive terms of the form x1, . . . , xm, x1, . . . , xm. A century ago Thue showed that there exist arbitrarily long square-free sequences using only three symbols. Sequences can be thought of as colors on the vertices of a path. Following the paper of Alon, Grytczuk, Ha luszczak and Riordan, w...
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In this paper we give a polynomial time algorithm which determines if a given graph containing a triangle and no induced seven-vertex path is 3-colorable, and gives an explicit coloring if one exists. This is the second paper in a series of two. The first one, [3] is also submitted to this journal. In [2, 3], a polynomial time algorithm is given for three-coloring triangle-free graphs with no i...
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ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2019
ISSN: 0895-4801,1095-7146
DOI: 10.1137/18m1190653