# Journal of Combinatorial Optimization

Journal of Combinatorial Optimization > 2018 > 36 > 2 > 508-531

Journal of Combinatorial Optimization > 2018 > 36 > 2 > 532-548

*G*is the minimum

*k*such that there exist

*k*independent sets $$\mathtt {N}_i\subseteq V$$ Ni⊆V , $$1\le i\le k$$ 1≤i≤k , such that the graph $$G'$$ G′ obtained from

*G*by adding some new edges between certain vertices inside the sets $$\mathtt {N}_i$$ Ni , $$1\le i\le k$$...

Journal of Combinatorial Optimization > 2018 > 36 > 2 > 329-345

Journal of Combinatorial Optimization > 2018 > 36 > 2 > 346-364

*G*is a partition of

*V*(

*G*) into $$V_1, \ldots , V_k$$ V1,…,Vk such that for every

*i*, $$1\le i\le k, G[V_i]$$ 1≤i≤k,G[Vi] has maximum degree at most $$c_i$$ ci . We prove that all planar graphs without 4-cycles and no less than two edges between triangles are (2, 0, 0)-colorable.

Journal of Combinatorial Optimization > 2018 > 36 > 2 > 591-616

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 > 36 > 2 > 434-457

*n*sensors with adjustable coverage radii deployed along a line interval or circle. Our goal is to determine a range assignment $$\mathbf {R}=({r_{1}},{r_{2}}, \ldots , {r_{n}})$$ R=(r1,r2,…,rn)...

Journal of Combinatorial Optimization > 2018 > 36 > 2 > 549-571

Journal of Combinatorial Optimization > 2018 > 36 > 2 > 493-507

Journal of Combinatorial Optimization > 2018 > 36 > 2 > 400-415

Journal of Combinatorial Optimization > 2018 > 36 > 2 > 572-590

*b-disjunctive dominating set*of the graph $$G=(V,E)$$ G=(V,E) if for every vertex $$v\in V{\setminus }D$$ v∈V\D ,

*v*is either adjacent to a vertex of

*D*or has at least

*b*vertices in

*D*at distance 2 from it. The Minimum

*b*-Disjunctive Domination Problem (MbDDP) is to find a

*b*-disjunctive dominating set of minimum cardinality...

Journal of Combinatorial Optimization > 2018 > 36 > 2 > 617-636

Journal of Combinatorial Optimization > 2018 > 36 > 2 > 392-399

Journal of Combinatorial Optimization > 2018 > 36 > 2 > 472-492

*m*identical parallel machines to minimize makespan, i.e., the maximum completion time of the jobs, where

*m*is given in advance and the jobs arrive online over time. We assume that the jobs, which arrive at some nonnegative real times, are of equal-length and are restricted by chain precedence constraints. Moreover, the jobs arriving at distinct times are independent,...

Journal of Combinatorial Optimization > 2018 > 36 > 2 > 416-433

*G*be a graph with vertex set

*V*and no isolated vertices, and let

*S*be a dominating set of

*V*. The set

*S*is a semitotal dominating set of

*G*if every vertex in

*S*is within distance 2 of another vertex of

*S*. And,

*S*is a semipaired dominating set of

*G*if

*S*can be partitioned into 2-element subsets such that the vertices in each 2-set are at most distance two apart. The semitotal domination number $$\gamma...

Journal of Combinatorial Optimization > 2018 > 36 > 2 > 637-669

*the imbalance*of the orientation, i.e. the higher it gets, the more imbalanced the orientation is. The studied problem is denoted by $${{\mathrm{\textsc {MaxIm}}}}$$ MAXIM . We first characterize...

Journal of Combinatorial Optimization > 2018 > 36 > 2 > 365-391

*n*cooperating robots traveling along predetermined closed and disjoint trajectories. Each robot needs to periodically communicate information to nearby robots. At places where two trajectories are within range of each other, a communication link is established, allowing two...