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- W2015334554 abstract "Given a graph G , let a k -trestle of G be a 2-connected spanning subgraph of G of maximum degree at most k . Also, let χ ( G ) be the Euler characteristic of G . This paper shows that every 3-connected graph G has a (10−2 χ ( G ))-trestle. If χ ( G )⩽−5, this is improved to 8−2 χ ( G ), and for χ ( G )⩽−10, this is further improved to 6−2 χ ( G ). This result is shown to be best possible for almost all values of χ ( G ) by the demonstration of 3-connected graphs embedded on each surface of Euler characteristic χ ⩽0 which have no (5−2 χ )-trestle. Also, it is shown that a 4-connected graph embeddable on a surface with non-negative Euler characteristic has a 3-trestle, approaching a conjecture of Nash-Williams." @default.
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- W2015334554 date "1998-09-01" @default.
- W2015334554 modified "2023-09-27" @default.
- W2015334554 title "On 2-Connected Spanning Subgraphs with Low Maximum Degree" @default.
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- W2015334554 doi "https://doi.org/10.1006/jctb.1998.1836" @default.
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