Note on 2-edge-colorings of complete graphs with small monochromatic k-connected subgraphs
Bollobás and Gyárfás conjectured that for n > 4 ( k − 1) every 2-edge-coloring of K n contains a monochromatic k -connected subgraph with at least n − 2 k + 2 vertices. Liu, et al. proved that the conjecture holds when n ≥ 13 k − 15. In this note, we characterize all the 2-edge-colorings of K n w...
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| Published in | Applied Mathematics-A Journal of Chinese Universities Vol. 29; no. 2; pp. 249 - 252 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Heidelberg
Editorial Committee of Applied Mathematics - A Journal of Chinese Universities
01.06.2014
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| Subjects | |
| Online Access | Get full text |
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| Abstract | Bollobás and Gyárfás conjectured that for
n
> 4 (
k
− 1) every 2-edge-coloring of
K
n
contains a monochromatic
k
-connected subgraph with at least
n
− 2
k
+ 2 vertices. Liu, et al. proved that the conjecture holds when
n
≥ 13
k
− 15. In this note, we characterize all the 2-edge-colorings of
K
n
where each monochromatic
k
-connected subgraph has at most
n
−2
k
+2 vertices for
n
≥ 13
k
− 15. |
|---|---|
| AbstractList | Bollobás and Gyárfás conjectured that for
n
> 4 (
k
− 1) every 2-edge-coloring of
K
n
contains a monochromatic
k
-connected subgraph with at least
n
− 2
k
+ 2 vertices. Liu, et al. proved that the conjecture holds when
n
≥ 13
k
− 15. In this note, we characterize all the 2-edge-colorings of
K
n
where each monochromatic
k
-connected subgraph has at most
n
−2
k
+2 vertices for
n
≥ 13
k
− 15. |
| Author | Jin, Ze-min Wen, Shi-li Wang, Yu-ling |
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| Cites_doi | 10.1016/j.disc.2007.09.031 10.1002/jgt.20365 10.1007/BF02579271 10.1016/j.disc.2006.01.030 10.1007/s00373-008-0811-y 10.1016/j.disc.2007.06.008 10.37236/502 |
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| Keywords | monochromatic subgraph connected subgraph 2-edge-coloring 05C35 05C15 |
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| References | Gyárfás, Sárközy (CR6) 2008; 308 Füredi (CR4) 1981; 1 Liu, Morris, Prince (CR9) 2008; 308 Burr (CR2) 1992 Gyárfás, Sárközy (CR5) 2008; 24 Bollobás, Gyárfás (CR1) 2008; 308 CR7 Fujita, Magnant (CR3) 2011; 18 Liu, Morris, Prince (CR8) 2008; 61 S Fujita (2859_CR3) 2011; 18 SA Burr (2859_CR2) 1992 H Liu (2859_CR9) 2008; 308 A Gyárfás (2859_CR6) 2008; 308 2859_CR7 B Bollobás (2859_CR1) 2008; 308 Z Füredi (2859_CR4) 1981; 1 H Liu (2859_CR8) 2008; 61 A Gyárfás (2859_CR5) 2008; 24 |
| References_xml | – volume: 308 start-page: 5096 year: 2008 end-page: 5121 ident: CR9 article-title: Highly connected multicolored subgraphs of multicolored graphs publication-title: Discrete Math doi: 10.1016/j.disc.2007.09.031 – volume: 18 start-page: #P15 issue: 1 year: 2011 ident: CR3 article-title: Note on highly connected monochromatic subgraph in 2-colored complete graphs publication-title: Electron J Combin – ident: CR7 – volume: 61 start-page: 22 year: 2008 end-page: 44 ident: CR8 article-title: Highly connected monochromatic subgraphs of multicolored graphs publication-title: J Graph Theory doi: 10.1002/jgt.20365 – year: 1992 ident: CR2 article-title: Either a graph or its complement contains a spanning broom publication-title: manuscript – volume: 1 start-page: 155 year: 1981 end-page: 162 ident: CR4 article-title: Maximum degree and fractional matchings in uniform hypergraphs publication-title: Combinatorica doi: 10.1007/BF02579271 – volume: 308 start-page: 1722 year: 2008 end-page: 1725 ident: CR1 article-title: Highly connected monochromatic subgraphs publication-title: Discrete Math doi: 10.1016/j.disc.2006.01.030 – volume: 24 start-page: 531 year: 2008 end-page: 536 ident: CR5 article-title: Size of monochromatic double stars in edge colorings publication-title: Graphs Combin doi: 10.1007/s00373-008-0811-y – volume: 308 start-page: 2620 year: 2008 end-page: 2622 ident: CR6 article-title: Size of monochromatic components in local edge colorings publication-title: Discrete Math doi: 10.1016/j.disc.2007.06.008 – volume: 308 start-page: 2620 year: 2008 ident: 2859_CR6 publication-title: Discrete Math doi: 10.1016/j.disc.2007.06.008 – volume: 308 start-page: 1722 year: 2008 ident: 2859_CR1 publication-title: Discrete Math doi: 10.1016/j.disc.2006.01.030 – volume: 61 start-page: 22 year: 2008 ident: 2859_CR8 publication-title: J Graph Theory doi: 10.1002/jgt.20365 – volume: 24 start-page: 531 year: 2008 ident: 2859_CR5 publication-title: Graphs Combin doi: 10.1007/s00373-008-0811-y – volume: 308 start-page: 5096 year: 2008 ident: 2859_CR9 publication-title: Discrete Math doi: 10.1016/j.disc.2007.09.031 – volume-title: manuscript year: 1992 ident: 2859_CR2 – volume: 18 start-page: #P15 issue: 1 year: 2011 ident: 2859_CR3 publication-title: Electron J Combin doi: 10.37236/502 – volume: 1 start-page: 155 year: 1981 ident: 2859_CR4 publication-title: Combinatorica doi: 10.1007/BF02579271 – ident: 2859_CR7 |
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| Snippet | Bollobás and Gyárfás conjectured that for
n
> 4 (
k
− 1) every 2-edge-coloring of
K
n
contains a monochromatic
k
-connected subgraph with at least
n
− 2
k
+ 2... |
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| StartPage | 249 |
| SubjectTerms | Applications of Mathematics Mathematics Mathematics and Statistics |
| Title | Note on 2-edge-colorings of complete graphs with small monochromatic k-connected subgraphs |
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