1pc Cartoon Design Water Bottle

1pc Cartoon Design Water Bottle


Children

Looking for a fun and unique water bottle for your child? Look no further than our 1pc Cartoon Design Water Bottle! Made with durable and safe materials, this water bottle is perfect for kids on the go! Our water bottles feature an amazing cartoon design, which will get kids wanting to use this product again and again! This water bottle comes in a variety of colors, such as black, green and blue. The water bottle measures 16cm in diameter and is suitable for kids up to the age of 2+. Kids love the different colors and the fun design this product offers, making it easy to grab for the next snack or school trip. As the water bottle is safe and BPA/Phthalate free, this is a product worth investing in! This product comes in 3 fun designs – Red, Blue and Green. Made of BPA/ Phthalate free non-toxic water bottle with lid, is suitable for kids up to the age of 2 years. Features: Material:Plastic Color:Multi-color Available:3 designs:Red, Blue, Green Size:16cm diameterQ:

How does the value of an Eulerian path to a Hamiltonian graph change when the graph is connected?

Suppose that $G=(V,E)$ is a connected graph, $Tsubseteq E$ a spanning tree of $G$ and $(C_1,…, C_k)in V^{(k)}$ a set of disjoint cycles of $G$ such that, $Tcup C_1cup.. cup C_n$ is a spanning subgraph of $G$.
I think that there exists an Eulerian hamiltonian path of $G$ such that all the cycles that it crosses are exactly $C_1,…, C_k$ because the spanning subgraph $Tcup C_1cup.. cup C_n$ of $G$ is hamiltonian (maybe it’s even an Eulerian graph).
So, I’m wondering (and I cannot find a reference) : what can I say about $Pin E(G)$ an Eulerian path of $G$ such that $Pcap C_j ne varnothing$?

A:

If $P$ is an Eulerian path and $C_i$ is not a bridge, then there is a natural partial order on the edges of $P$, inherited from $G$: between any two edges in $C_i$, there is the corresponding bridge that separates them.

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