Geodesic
Connected even factors in the square of essentially 2-edge-connected graph
Jan Ekstein1 ; Baoyindureng Wu2 ; Liming Xiong3
1University of West Bohemia
2Xinjiang University
3Beijing Institute of Technology
The electronic journal of combinatorics, Tome 24 (2017) no. 3
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An essentially $k$-edge connected graph $G$ is a connected graph such that deleting less than $k$ edges from $G$ cannot result in two nontrivial components. In this paper we prove that if an essentially 2-edge-connected graph $G$ satisfies that for any pair of leaves at distance 4 in $G$ there exists another leaf of $G$ that has distance 2 to one of them, then the square $G^2$ has a connected even factor with maximum degree at most 4. Moreover we show that, in general, the square of essentially 2-edge-connected graph does not contain a connected even factor with bounded maximum degree.
DOI : 10.37236/5467
Classification : 05C40, 05C38
Mots-clés : connected even factors, essentially 2-edge connected graphs, square of graphs

Jan Ekstein  1   ; Baoyindureng Wu  2   ; Liming Xiong  3

1 University of West Bohemia
2 Xinjiang University
3 Beijing Institute of Technology 
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Jan Ekstein; Baoyindureng Wu; Liming Xiong. Connected even factors in the square of essentially 2-edge-connected graph. The electronic journal of combinatorics, Tome 24 (2017) no. 3. doi: 10.37236/5467

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