The Ramsey numbers for certain large trees of order n with maximum degree at most n − 6 versus the wheel of order nine

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2025-03-04 DOI:10.1016/j.disc.2025.114461

Thomas Britz , Zhi Yee Chng , Kok Bin Wong

引用次数: 0

Abstract

For a fixed positive integer

k \geq 5

, the Ramsey numbers

R (T_{n}, W_{8})

are determined for the tree

T_{n}

of sufficiently large order n and maximum degree

Δ (T_{n}) = n - k - 1

. This result provides a partial proof for the conjecture, due to Chen, Zhang and Zhang and to Hafidh and Baskoro, that

R (T_{n}, W_{m}) = 2 n - 1

for each tree

T_{n}

of order

n \geq m - 1

with

Δ (T_{n}) \leq n - m + 2

when

m \geq 4

is even, for the case when

m = 8

and n is sufficiently large.

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来源期刊

Discrete Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

期刊介绍： Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.

The Ramsey numbers for certain large trees of order n with maximum degree at most n − 6 versus the wheel of order nine

Abstract

The Ramsey numbers for certain large trees of order n with maximum degree at most n − 6 versus the wheel of order nine