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- W2793740929 abstract "For two given graphs $G_{1}$ and $G_{2}$ , the planar Ramsey number $PR(G_{1},G_{2})$ is the smallest integer $N$ such that every planar graph $G$ on $N$ vertices either contains $G_{1}$ , or its complement contains $G_{2}$ . Let $C_{4}$ be a quadrilateral, $T_{n}$ a tree of order $ngeq 3$ with maximum degree $k$ , and $K_{1,k}$ a star of order $k+1$ . We show that $PR(C_{4},T_{n})=max {n+1,PR(C_{4},K_{1,k})}$ . Combining this with a result of Chen et al. [‘All quadrilateral-wheel planar Ramsey numbers’, Graphs Combin. 33 (2017), 335–346] yields exact values of all the quadrilateral-tree planar Ramsey numbers." @default.
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- W2793740929 date "2018-01-30" @default.
- W2793740929 modified "2023-09-27" @default.
- W2793740929 title "QUADRILATERAL-TREE PLANAR RAMSEY NUMBERS" @default.
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- W2793740929 doi "https://doi.org/10.1017/s0004972717001022" @default.
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