A star-comb lemma for infinite digraphs
The star-comb lemma is a fundamental tool in infinite graph theory, which states that for any infinite set $U$ of vertices in a connected graph $G$ there exists either a subdivided infinite star in $G$ with all leaves in $U$, or an infinite comb in $G$ with all teeth in $U$. In this paper, we elabor...
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| creator | Reich, Florian |
| description | The star-comb lemma is a fundamental tool in infinite graph theory, which
states that for any infinite set $U$ of vertices in a connected graph $G$ there
exists either a subdivided infinite star in $G$ with all leaves in $U$, or an
infinite comb in $G$ with all teeth in $U$.
In this paper, we elaborate a pendant of the star-comb lemma for directed
graphs. More precisely, we prove that for any infinite set $U$ of vertices in a
strongly connected directed graph $D$, there exists a strongly connected
substructure of $D$ attached to infinitely many vertices of $U$ that is either
shaped by a star or shaped by a comb, or is a chain of triangles. |
| doi_str_mv | 10.48550/arxiv.2406.04877 |
| format | Article |
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states that for any infinite set $U$ of vertices in a connected graph $G$ there
exists either a subdivided infinite star in $G$ with all leaves in $U$, or an
infinite comb in $G$ with all teeth in $U$.
In this paper, we elaborate a pendant of the star-comb lemma for directed
graphs. More precisely, we prove that for any infinite set $U$ of vertices in a
strongly connected directed graph $D$, there exists a strongly connected
substructure of $D$ attached to infinitely many vertices of $U$ that is either
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states that for any infinite set $U$ of vertices in a connected graph $G$ there
exists either a subdivided infinite star in $G$ with all leaves in $U$, or an
infinite comb in $G$ with all teeth in $U$.
In this paper, we elaborate a pendant of the star-comb lemma for directed
graphs. More precisely, we prove that for any infinite set $U$ of vertices in a
strongly connected directed graph $D$, there exists a strongly connected
substructure of $D$ attached to infinitely many vertices of $U$ that is either
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states that for any infinite set $U$ of vertices in a connected graph $G$ there
exists either a subdivided infinite star in $G$ with all leaves in $U$, or an
infinite comb in $G$ with all teeth in $U$.
In this paper, we elaborate a pendant of the star-comb lemma for directed
graphs. More precisely, we prove that for any infinite set $U$ of vertices in a
strongly connected directed graph $D$, there exists a strongly connected
substructure of $D$ attached to infinitely many vertices of $U$ that is either
shaped by a star or shaped by a comb, or is a chain of triangles.</abstract><doi>10.48550/arxiv.2406.04877</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Combinatorics |
| title | A star-comb lemma for infinite digraphs |
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