A graph is said to be K1,4-free if it does not contain an induced subgraph isomorphic to K1,4. Let κ be an integer with κ ≥ 2. We prove that if G is a K1,4-free graph of order at least llκ- 10 with minimum degree ...A graph is said to be K1,4-free if it does not contain an induced subgraph isomorphic to K1,4. Let κ be an integer with κ ≥ 2. We prove that if G is a K1,4-free graph of order at least llκ- 10 with minimum degree at least four, then G contains k vertex-disjoint copies of K1 ＋ （K1 ∪ KK2）.展开更多
A graph is said to be claw-free if it does not contain an induced subgraph isomorphic to K1,3. Let K4 be the graph obtained by removing exactly one edge from K4 and let k be an integer with k ≥ 2. We prove that if G ...A graph is said to be claw-free if it does not contain an induced subgraph isomorphic to K1,3. Let K4 be the graph obtained by removing exactly one edge from K4 and let k be an integer with k ≥ 2. We prove that if G is a claw-free graph of order at least 13k - 12 and with minimum degree at least five, then G contains k vertex-disjoint copies of K4. The requirement of number five is necessary.展开更多
基金Supported by National Natural Science Foundation of China(Grant Nos.11161035 and 11226292)Ningxia Ziran(Grant No.NZ1153)research grant from Ningxia University(Grant No.zr1122)
文摘A graph is said to be K1,4-free if it does not contain an induced subgraph isomorphic to K1,4. Let κ be an integer with κ ≥ 2. We prove that if G is a K1,4-free graph of order at least llκ- 10 with minimum degree at least four, then G contains k vertex-disjoint copies of K1 ＋ （K1 ∪ KK2）.
基金This work was supported in part by the National Natural Science Foundation of China （Grant Nos. 11161035, 11401455） and the Fundamental Research Funds for the Central Universities （No. K5051370010）.
文摘A graph is said to be claw-free if it does not contain an induced subgraph isomorphic to K1,3. Let K4 be the graph obtained by removing exactly one edge from K4 and let k be an integer with k ≥ 2. We prove that if G is a claw-free graph of order at least 13k - 12 and with minimum degree at least five, then G contains k vertex-disjoint copies of K4. The requirement of number five is necessary.
