# Ramsey Good Graphs with Long Suspended Paths

Ramsey Good Graphs with Long Suspended Paths Graphs and Combinatorics https://doi.org/10.1007/s00373-018-1910-z ORIGINAL PAPER 1 2 1 Chaoping Pei · Ming Chen · Yusheng Li · Pei Yu Received: 11 April 2016 / Revised: 15 May 2018 © Springer Japan KK, part of Springer Nature 2018 Abstract A connected graph H with |H|≥ σ(G) is said to be G-good if R(G, H ) = (χ (G) − 1)(|H|− 1) + σ(G). For an integer  ≥ 3, let P be a path of order , and () H a graph obtained from H by joining the end vertices of P to distinct vertices u,v of H . It is widely known that for any graphs G and H,if  is sufﬁciently large, () then H is G-good. In this note, we show that there exists a constant c = c() such that for any graphs G and H with (G) ≤  and (H ) ≤ ,if  ≥ c · (|G|+|H |), () 2 then H is G-good; and if n ≥ 2α(G) +  (G) + 4, then P is G-good. Keywords Ramsey number · Ramsey goodness · Suspended path 1 Introduction For graphs G and H,the Ramsey number R(G, H ) is deﬁned to http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Graphs and Combinatorics Springer Journals

# Ramsey Good Graphs with Long Suspended Paths

, Volume OnlineFirst – Jun 6, 2018
9 pages

/lp/springer_journal/ramsey-good-graphs-with-long-suspended-paths-le9tnnNqhy
Publisher
Springer Japan
Subject
Mathematics; Combinatorics; Engineering Design
ISSN
0911-0119
eISSN
1435-5914
D.O.I.
10.1007/s00373-018-1910-z
Publisher site
See Article on Publisher Site

### Abstract

Graphs and Combinatorics https://doi.org/10.1007/s00373-018-1910-z ORIGINAL PAPER 1 2 1 Chaoping Pei · Ming Chen · Yusheng Li · Pei Yu Received: 11 April 2016 / Revised: 15 May 2018 © Springer Japan KK, part of Springer Nature 2018 Abstract A connected graph H with |H|≥ σ(G) is said to be G-good if R(G, H ) = (χ (G) − 1)(|H|− 1) + σ(G). For an integer  ≥ 3, let P be a path of order , and () H a graph obtained from H by joining the end vertices of P to distinct vertices u,v of H . It is widely known that for any graphs G and H,if  is sufﬁciently large, () then H is G-good. In this note, we show that there exists a constant c = c() such that for any graphs G and H with (G) ≤  and (H ) ≤ ,if  ≥ c · (|G|+|H |), () 2 then H is G-good; and if n ≥ 2α(G) +  (G) + 4, then P is G-good. Keywords Ramsey number · Ramsey goodness · Suspended path 1 Introduction For graphs G and H,the Ramsey number R(G, H ) is deﬁned to

### Journal

Graphs and CombinatoricsSpringer Journals

Published: Jun 6, 2018

## You’re reading a free preview. Subscribe to read the entire article.

### DeepDyve is your personal research library

It’s your single place to instantly
that matters to you.

over 18 million articles from more than
15,000 peer-reviewed journals.

All for just \$49/month

### Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

### Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

### Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

### Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

DeepDyve

DeepDyve

### Pro

Price

FREE

\$49/month
\$360/year

Save searches from
PubMed

Create lists to

Export lists, citations