Motivated by parallel routing in networks with faults, we study the following graph theoretical problem. Let G be a graph of minimum vertex degree d. We say that G is strongly Menger-connected if for any copy G f of G with at most d -2 nodes removed, every pair of nodes u and v in G f are connected
Connectivity of Strong Products of Graphs
✍ Scribed by Simon Špacapan
- Publisher
- Springer Japan
- Year
- 2010
- Tongue
- English
- Weight
- 329 KB
- Volume
- 26
- Category
- Article
- ISSN
- 0911-0119
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Let G [XI H be the strong product of graphs G and H. We give a short proof that Kneser graphs are then used to demonstrate that this lower bound is sharp. We also prove that for every n > 2 there is an infinite sequence of pairs of graphs G and G' such that G' is not a retract of G while G' IXI K,
## Abstract We prove that the strong product of any at least ${({\rm ln}}\, {2})\Delta+{O}(\sqrt{\Delta})$ non‐trivial connected graphs of maximum degree at most Δ is pancyclic. The obtained result is asymptotically best possible since the strong product of ⌊(ln 2)__D__⌋ stars __K__~1,__D__~ is not