a path of length

USAGE SUMMARY

The phrase "a path of length" is correct and usable in written English.
It is typically used in mathematical or computational contexts, particularly in graph theory or algorithms, to describe the distance or number of edges in a path. Example: "In this graph, we need to find a path of length three that connects the specified nodes."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

49 human-written examples

Solutions to the NDPVC are subgraphs containing a path of length at most Hst for each commodity {s, t} and a path of length at most H′st between s and t after at most k−1 edge failures.

European Journal of Operational Research

In the example of Figure 2, we consider paths of lengths 0 and 1, where a path of length 0 corresponds to a single atom and a path of length 1 corresponds to a bond including its endpoint atoms.

Journal of Cheminformatics

Observe that a path of length l involves ((l+1)) elements of X that need not be distinct in general.

Fixed Point Theory and Applications

where we also include a path of length 0, which is a model containing only the modeled factor itself and no conditional factors.

EURASIP Journal on Audio, Speech, and Music Processing

A Steiner pentagon covering design (SPCD) of order n is a pair (Kn,B), where B is a collection of c(n)=⌈n/5⌈n−1/2⌉⌉ pentagons from Kn such that any two vertices are joined by a path of length 1 in at least one pentagon of B, and also by a path of length 2 in at least one pentagon of B. The existence of SPCDs is investigated.

Discrete Mathematics

Without loss of generality, we assume that (v_{1}v_{2}v_{3}v_{4}v_{5}v_{6}) is a path of length 5 in T. We now consider the following three cases.

Journal of Inequalities and Applications

Human-verified similar examples from authoritative sources

Similar Expressions

10 human-written examples

Recall that a rectifiable path is a path of finite length (see, e.g., [[5], p.34]).

Fixed Point Theory and Applications

A solution is a path of minimal length between these nodes.

Plosone

As the eccentric rotates with the shaft, it slides inside the strap, and the piston 4 moves on a straight path of length 2AB.

Encyclopedia Britannica

If (p=e_1ldots e_n) is a closed path of length (ge 1) and the vertices (s(e_1),ldots, s(e_n)) are distinct then we call the path p a cycle.

Bulletin of Mathematical Sciences

That is, we do not need to consider a bypassed path of length greater than 2.

BMC Systems Biology

Expert writing Tips

Best practice

When discussing graph theory or network analysis, be precise with your terminology. "A path of length n" specifically refers to a path with n edges (or steps), not n+1 vertices.

Common error

Avoid using "a path of length" when you actually mean the physical distance of the path. While related, length refers to the number of edges, while distance refers to the actual measure of how far it is from the start to the end point.

Linguistic Context

The phrase "a path of length" functions as a noun phrase, typically serving as an object or complement within a sentence. Ludwig shows its use in scientific and mathematical contexts to precisely define the extent of a route or sequence.

Expression frequency: Very common

Frequent in

Science

98%

Encyclopedias

1%

Formal & Business

1%

Less common in

News & Media

0%

Social Media

0%

Wiki

0%

Ludwig's WRAP-UP

In summary, "a path of length" is a grammatically correct noun phrase primarily used in scientific and mathematical domains. As Ludwig AI confirms, it serves to define the number of steps or segments in a route or connection. While the phrase is very common within its specific context, it's crucial to differentiate "length" (number of edges) from "distance" (physical measure). When writing, remember that the number of edges are what define length not the distance between nodes. Using alternatives like "a route of length" or "a distance of" can provide clarity depending on the intended meaning.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

a route of length

Replaces "path" with "route", emphasizing the journey or course taken.

a trajectory of length

Substitutes "path" with "trajectory", suggesting a more calculated or projected course.

a course of length

Similar to "route of length", "course" highlights a planned or designated path.

a distance of

Focuses on the measurable extent of the path rather than the path itself.

a segment of length

Highlights a portion or section of a longer path with a defined length.

a connection of length

Emphasizes the linking aspect of the path, specifying the length of the connection.

a traversal of length

Replaces "path" with "traversal", referring to the act of passing through or across something.

a span of length

Similar to "distance of", "span" refers to the extent or reach of the path.

a sequence of length

Emphasizes the sequential aspect of the path, representing it as an ordered series of steps.

a progression of length

Highlights the forward movement along the path, specifying the length of the progression.

FAQs

How do I use "a path of length" in a sentence?

Use "a path of length" to describe a route or sequence with a specific number of steps or segments. For example, "The algorithm searches for "a path of length" three between the two nodes."

What is an alternative to saying "a path of length"?

Depending on the context, you could use alternatives such as "a route of length", "a distance of", or "a segment of length".

What does "path length" mean in graph theory?

In graph theory, "path length" refers to the number of edges or steps in a path between two vertices. It's a discrete measure, unlike the physical distance of a path.

How is "a path of length" different from "path distance"?

"A path of length" describes the number of edges or connections in the path, while "path distance" measures the actual physical distance covered by the path, which might be a continuous value.