How Long to Read Proof of the 1-Factorization and Hamilton Decomposition Conjectures

How Long Does it Take to Read Proof of the 1-Factorization and Hamilton Decomposition Conjectures?

It takes the average reader 2 hours and 46 minutes to read Proof of the 1-Factorization and Hamilton Decomposition Conjectures by Béla Csaba

Assuming a reading speed of 250 words per minute. Learn more

Description

In this paper the authors prove the following results (via a unified approach) for all sufficiently large n: (i) [1-factorization conjecture] Suppose that n is even and D≥2⌈n/4⌉−1. Then every D-regular graph G on n vertices has a decomposition into perfect matchings. Equivalently, χ′(G)=D. (ii) [Hamilton decomposition conjecture] Suppose that D≥⌊n/2⌋. Then every D-regular graph G on n vertices has a decomposition into Hamilton cycles and at most one perfect matching. (iii) [Optimal packings of Hamilton cycles] Suppose that G is a graph on n vertices with minimum degree δ≥n/2. Then G contains at least regeven(n,δ)/2≥(n−2)/8 edge-disjoint Hamilton cycles. Here regeven(n,δ) denotes the degree of the largest even-regular spanning subgraph one can guarantee in a graph on n vertices with minimum degree δ. (i) was first explicitly stated by Chetwynd and Hilton. (ii) and the special case δ=⌈n/2⌉ of (iii) answer questions of Nash-Williams from 1970. All of the above bounds are best possible.

How long is Proof of the 1-Factorization and Hamilton Decomposition Conjectures?

Proof of the 1-Factorization and Hamilton Decomposition Conjectures by Béla Csaba is 164 pages long, and a total of 41,656 words.

This makes it 55% the length of the average book. It also has 51% more words than the average book.

How Long Does it Take to Read Proof of the 1-Factorization and Hamilton Decomposition Conjectures Aloud?

The average oral reading speed is 183 words per minute. This means it takes 3 hours and 47 minutes to read Proof of the 1-Factorization and Hamilton Decomposition Conjectures aloud.

What Reading Level is Proof of the 1-Factorization and Hamilton Decomposition Conjectures?

Proof of the 1-Factorization and Hamilton Decomposition Conjectures is suitable for students ages 10 and up.

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