Flows and generalized coloring theorems in graphs

Jaeger, François

doi:10.1016/0095-8956(79)90057-1

Cited by 218 publications

(130 citation statements)

References 13 publications

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“…By a well-known result of Jaeger [7,8], every 4-edge-connected graph G admits a spanning closed trail. It is easy to see that if the maximum degree of G is ∆, then such a trail gives rise to a ∆/2 -walk in G. For even ∆, this improves on the bound of Theorem 1 by one.…”

Section: Lemma 4 Letmentioning

confidence: 99%

A Note on k-walks in Bridgeless Graphs

Kaiser

Kužel

et al. 2007

Graphs and Combinatorics

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Section: Lemma 4 Letmentioning

confidence: 99%

A Note on k-walks in Bridgeless Graphs

Kaiser

Kužel

et al. 2007

Graphs and Combinatorics

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“…Jeager [4] showed that every 2-edge-connected graph has an 8-NZF, and Seymour [8] improved Jaeger's result by showing that every 2-edge-connected graph has a 6-NZF.…”

Section: ------------------mentioning

confidence: 97%

Nowhere‐zero 3‐flows in locally connected graphs

Lai¹

2003

Journal of Graph Theory

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Let G be a graph. For each vertex v 2V (G ), N v denotes the subgraph induces by the vertices adjacent to v in G. The graph G is locally kedge-connected if for each vertex v 2V (G ), N v is k-edge-connected. In this paper we study the existence of nowhere-zero 3-flows in locally k-edgeconnected graphs. In particular, we show that every 2-edge-connected, locally 3-edge-connected graph admits a nowhere-zero 3-flow. This result is best possible in the sense that there exists an infinite family of 2-edgeconnected, locally 2-edge-connected graphs each of which does not have a 3-NZF. ß

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“…This was used by Itai, Lipton, Papadimitrou and Rodeh [71] to obtain Jaeger's result [73,74] on the existence of a cycle double cover of the edges of a 4-edge connected graph G as follows: for each spanning tree T i , they construct an even subgraph H i containing E(G) − E(T i ); so with two disjoint trees T 1 and T 2 they get a cover of all the edges by H 1 ∪ H 2 , as an edge of G not covered should be in both E(T 1 ) and E(T 2 ). It follows that {H 1 , H 2 , H 1 △H 2 }, where H 1 △H 2 denotes the symmetric difference of H 1 and H 2 , gives a cycle double cover of E(G).…”

Section: Theorem 1 ([135])mentioning

confidence: 99%

“…For Eulerian graphs see the work of Jaeger [73,74], the book of Fleischner [55,56], the book of C.Q. Zhang [154], the survey of Lesniak and Oellermann [95] or that of Catlin [31].…”

Section: Theorem 20 ([15])mentioning

confidence: 99%