# Search results for: Xueliang Li

Journal of Combinatorial Optimization > 2018 > 36 > 2 > 458-471

*T*in an edge-colored graph is called a

*proper tree*if no two adjacent edges of

*T*receive the same color. Let

*G*be a connected graph of order

*n*and

*k*be an integer with $$2\le k \le n$$ 2≤k≤n . For $$S\subseteq V(G)$$ S⊆V(G) and $$|S| \ge 2$$ |S|≥2 , an

*S*-

*tree*is a tree containing the vertices of

*S*in

*G*. A set $$\{T_1,T_2,\ldots ,T_\ell \}$$ {T1,T2,…,Tℓ} of

*S*-trees is called

*internally disjoint*...

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...

Journal of Combinatorial Optimization > 2017 > 34 > 2 > 441-452

*G*is a function $$f:V\rightarrow N$$ f : V → N such that $$f(x)\ne f(y)$$ f ( x ) ≠ f ( y ) for every edge $$xy\in E$$ x y ∈ E . A proper coloring of a graph

*G*such that for every $$k\ge 1$$ k ≥ 1 , the union of any

*k*color classes induces a $$(k-1)$$ ( k - 1 ) -degenerate...

Journal of Combinatorial Optimization > 2017 > 34 > 1 > 165-173

*G*, the smallest number of colors that are needed in order to make

*G*proper connected is called the proper connection number of...

Journal of Combinatorial Optimization > 2017 > 33 > 4 > 1443-1453

*T*in an edge-colored (vertex-colored) graph

*H*is called a

*monochromatic (vertex-monochromatic) tree*if all the edges (internal vertices) of

*T*have the same color. For $$S\subseteq V(H)$$ S ⊆ V ( H ) , a

*monochromatic (vertex-monochromatic) S-tree*in

*H*is a monochromatic (vertex-monochromatic) tree of

*H*containing the vertices of

*S*. For a connected graph

*G*and a given integer

*k*with...

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

Journal of Combinatorial Optimization > 2016 > 32 > 1 > 260-266

*total-colored graph*is a graph such that both all edges and all vertices of the graph are colored. A path in a total-colored graph is a

*total rainbow path*if its edges and internal vertices have distinct colors. A total-colored graph is

*total-rainbow connected*if any two vertices of the graph are connected by a total-rainbow path of the graph. For a connected graph $$G$$ G , the

*total rainbow connection number*...

Journal of Combinatorial Optimization > 2016 > 31 > 1 > 223-238

Journal of Combinatorial Optimization > 2017 > 33 > 1 > 275-282

*k*-connectivity $$\kappa _k(G)$$ κ k ( G ) of a graph

*G*was introduced by Chartrand et al. in (Bull Bombay Math Colloq 2:1–6, 1984), which is a nice generalization of the classical connectivity. Recently, as a natural counterpart, Li et al. proposed the concept of generalized edge-connectivity for a graph. In this paper, we consider the computational complexity of the...

Journal of Combinatorial Optimization > 2017 > 33 > 1 > 283-291

*k*-connectivity $$\kappa '_{k}(G)$$ κ k ′ ( G ) of a graph

*G*, introduced by Chartrand in 1984, is a generalization of the cut-version of the classical connectivity. Another generalized connectivity of a graph

*G*, named the generalized

*k*-connectivity $$\kappa _{k}(G)$$ κ k ( G ) , mentioned by Hager in 1985, is a natural generalization of the path-version of...

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...

Journal of Combinatorial Optimization > 2012 > 24 > 3 > 389-396

*G*be a nontrivial connected graph of order

*n*and let

*k*be an integer with 2≤

*k*≤

*n*. For a set

*S*of

*k*vertices of

*G*, let

*κ*(

*S*) denote the maximum number

*ℓ*of edge-disjoint trees

*T*

_{1},

*T*

_{2},…,

*T*

_{ ℓ }in

*G*such that

*V*(

*T*

_{ i })∩

*V*(

*T*

_{ j })=

*S*for every pair

*i*,

*j*of distinct integers with 1≤

*i*,

*j*≤

*ℓ*. Chartrand et al. generalized the concept of connectivity as follows: The

*k*-

*connectivity*, denoted by

*κ*

_{ k }(

*G*), of

*G*is...

Journal of Combinatorial Optimization > 2006 > 11 > 4 > 445-454

*NP*-complete...

Journal of Combinatorial Optimization > 2005 > 9 > 4 > 331-347

*O*(

*n*

^{5}) combinatorial algorithm for the minimum weighted coloring problem on claw-free perfect graphs, which was posed by Hsu and Nemhauser in 1984. Our algorithm heavily relies on the structural descriptions of claw-free perfect graphs given by Chavátal and Sbihi and by Maffray and Reed.