Geodesic
Decomposing a signed graph into rooted circuits
Advances in Combinatorics (2024)
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We prove a precise min-max theorem for the following problem. Let $G$ be an Eulerian graph with a specified set of edges $S \subseteq E(G)$, and let $b$ be a vertex of $G$. Then what is the maximum integer $k$ so that the edge-set of $G$ can be partitioned into $k$ non-zero $b$-trails? That is, each trail must begin and end at $b$ and contain an odd number of edges from~$S$. This theorem is motivated by a connection to vertex-minors and yields two conjectures of Máčajová and Škoviera as corollaries.
Publié le : 
@article{ADVC_2024_a0,
     author = {Rose McCarty},
     title = {Decomposing a signed graph into rooted circuits},
     journal = {Advances in Combinatorics},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADVC_2024_a0/}
}
TY  - JOUR
AU  - Rose McCarty
TI  - Decomposing a signed graph into rooted circuits
JO  - Advances in Combinatorics
PY  - 2024
UR  - http://geodesic.mathdoc.fr/item/ADVC_2024_a0/
LA  - en
ID  - ADVC_2024_a0
ER  - 
%0 Journal Article
%A Rose McCarty
%T Decomposing a signed graph into rooted circuits
%J Advances in Combinatorics
%D 2024
%U http://geodesic.mathdoc.fr/item/ADVC_2024_a0/
%G en
%F ADVC_2024_a0
Rose McCarty. Decomposing a signed graph into rooted circuits. Advances in Combinatorics (2024). http://geodesic.mathdoc.fr/item/ADVC_2024_a0/