# Search results for: Qingqiong Cai

Journal of Combinatorial Optimization > 2018 > 35 > 4 > 1300-1311

*vertex-monochromatic path*if its internal vertices have the same color. A vertex-coloring of a graph is a

*monochromatic vertex-connection coloring*(

*MVC-coloring*for short), if there is a vertex-monochromatic path joining any two vertices in the graph. For a connected graph

*G*, the

*monochromatic vertex-connection number*, denoted by

*mvc*(

*G*), is defined to be...

Discrete Applied Mathematics > 2016 > 209 > C > 68-74

Bulletin of the Malaysian Mathematical Sciences Society > 2016 > 39 > 3 > 1225-1236

*G*is said to be a rainbow tree if no two edges on the tree share the same color. Given two positive integers

*k*, $$\ell $$ ℓ with $$k\ge 3$$ k ≥ 3 , the $$(k,\ell )$$ ( k , ℓ ) -

*rainbow index*$$rx_{k,\ell }(G)$$ r x k , ℓ ( G ) of

*G*is the minimum number of colors needed in an edge-coloring of

*G*such that for any set

*S*of...

Bulletin of the Malaysian Mathematical Sciences Society > 2016 > 39 > 2 > 765-771

*G*is said to be a rainbow tree if no two edges on the tree share the same color. Given two positive integers

*k*, $$\ell $$ ℓ with $$k\ge 3$$ k ≥ 3 , the $$(k,\ell )$$ ( k , ℓ )

*-rainbow index*$$rx_{k,\ell }(G)$$ r x k , ℓ ( G ) of

*G*is the minimum number of colors needed in an edge-coloring of

*G*such that for any set

*S*of...

Journal of Combinatorial Optimization > 2016 > 31 > 3 > 1142-1159

Journal of Combinatorial Optimization > 2017 > 33 > 1 > 123-131

*monochromatic path*if all the edges on the path are colored with one same color. An edge-coloring of

*G*is a

*monochromatic connection coloring*(MC-coloring, for short) if there is a monochromatic path joining any two vertices in

*G*. For a connected graph

*G*, the

*monochromatic connection number*of

*G*, denoted by

*mc*(

*G*), is defined to be the maximum number of colors...

*G*was introduced by Chartrand et al. (Network 54(2) (2009), 75–81; 55 (2010), 360–367). For the complete graph

*K*

_{n}of order $n\ge 6$, they showed that $r{x}_{3,\ell}\left({K}_{n}\right)=3$ for $\ell =1,2$. Furthermore, they conjectured that for every positive integer $\ell $, there exists a positive integer

*N*such that $r{x}_{3,\ell}\left({K}_{n}\right)=3$ for every integer $n\ge N$. More generally, they conjectured that for every...