Restricted size Ramsey number for path of order three versus graph of order five
Let $G$ and $H$ be simple graphs. The Ramsey number for a pair of graph $G$ and $H$ is the smallest number $r$ such that any red-blue coloring of edges of $K_r$ contains a red subgraph $G$ or a blue subgraph $H$. The size Ramsey number for a pair of graph $G$ and $H$ is the smallest number $\hat{r}$...
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GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB,
2017-04-10.
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| LEADER | 03030 am a22002653u 4500 | ||
|---|---|---|---|
| 001 | EJGTA_356_pdf_45 | ||
| 042 | |a dc | ||
| 100 | 1 | 0 | |a Silaban, Denny Riama; Combinatorial Mathematics Research Group Faculty of Mathematics and Natural Sciences Institut Teknologi Bandung Jalan Ganesa 10 Bandung, Indonesia |e author |
| 100 | 1 | 0 | |a Research Grant "Program Penelitian Unggulan Perguruan Tinggi", Ministry of Research, Technology, and Higher Education, Indonesia. |e contributor |
| 700 | 1 | 0 | |a Baskoro, Edy Tri; Combinatorial Mathematics Research Group Faculty of Mathematics and Natural Sciences Institut Teknologi Bandung Jalan Ganesa 10 Bandung, Indonesia |e author |
| 700 | 1 | 0 | |a Uttunggadewa, Saladin; Combinatorial Mathematics Research Group Faculty of Mathematics and Natural Sciences Institut Teknologi Bandung Jalan Ganesa 10 Bandung, Indonesia |e author |
| 245 | 0 | 0 | |a Restricted size Ramsey number for path of order three versus graph of order five |
| 260 | |b GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, |c 2017-04-10. | ||
| 500 | |a https://www.ejgta.org/index.php/ejgta/article/view/356 | ||
| 520 | |a Let $G$ and $H$ be simple graphs. The Ramsey number for a pair of graph $G$ and $H$ is the smallest number $r$ such that any red-blue coloring of edges of $K_r$ contains a red subgraph $G$ or a blue subgraph $H$. The size Ramsey number for a pair of graph $G$ and $H$ is the smallest number $\hat{r}$ such that there exists a graph $F$ with size $\hat{r}$ satisfying the property that any red-blue coloring of edges of $F$ contains a red subgraph $G$ or a blue subgraph $H$. Additionally, if the order of $F$ in the size Ramsey number is $r(G,H)$, then it is called the restricted size Ramsey number. In 1983, Harary and Miller started to find the (restricted) size Ramsey number for any pair of small graphs with order at most four. Faudree and Sheehan (1983) continued Harary and Miller's works and summarized the complete results on the (restricted) size Ramsey number for any pair of small graphs with order at most four. In 1998, Lortz and Mengenser gave both the size Ramsey number and the restricted size Ramsey number for any pair of small forests with order at most five. To continue their works, we investigate the restricted size Ramsey number for a path of order three versus connected graph of order five. | ||
| 540 | |a Copyright (c) 2017 Electronic Journal of Graph Theory and Applications (EJGTA) | ||
| 546 | |a eng | ||
| 690 | |a restricted size Ramsey number, path, connected graph | ||
| 655 | 7 | |a info:eu-repo/semantics/article |2 local | |
| 655 | 7 | |a info:eu-repo/semantics/publishedVersion |2 local | |
| 655 | 7 | |a Peer-reviewed Article |2 local | |
| 786 | 0 | |n Electronic Journal of Graph Theory and Applications (EJGTA); Vol 5, No 1 (2017): Electronic Journal of Graph Theory and Applications; 155-162 | |
| 786 | 0 | |n 2338-2287 | |
| 787 | 0 | |n https://www.ejgta.org/index.php/ejgta/article/view/356/pdf_45 | |
| 856 | 4 | 1 | |u https://www.ejgta.org/index.php/ejgta/article/view/356/pdf_45 |z Get Fulltext |