最大度不超过n的n阶大树 − 6与9阶轮盘的Ramsey数

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

摘要

对于固定正整数k≥5，对于足够大阶n且最大阶Δ(Tn)=n−k−1的树Tn，确定了拉姆齐数R（Tn,W8）。该结果部分证明了由Chen、Zhang和Zhang以及Hafidh和Baskoro提出的猜想，即当m≥4为偶数时，当m=8且n足够大时，对于阶n≥m - 1且Δ(Tn)≤n - m+2的每棵树Tn， R(Tn,Wm)=2n - 1。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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

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.

最大度不超过n的n阶大树 − 6与9阶轮盘的Ramsey数

摘要

最大度不超过n的n阶大树 − 6与9阶轮盘的Ramsey数