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Nordhaus–Gaddum-type results for path covering and $$L(2,1)$$ -labeling numbers

Author

Listed:
  • Damei Lü

    (Nantong University)

  • Juan Du

    (Nantong University)

  • Nianfeng Lin

    (Nantong University)

  • Ke Zhang

    (Nantong University)

  • Dan Yi

    (Nantong University)

Abstract

A Nordhaus–Gaddum-type result is a (tight) lower or upper bound on the sum (or product) of a parameter of a graph and its complement. The path covering number $$c(G)$$ of a graph is the smallest number of vertex-disjoint paths needed to cover the vertices of the graph. For two positive integers $$j$$ and $$k$$ with $$j\ge k,$$ an $$L(j,k)$$ -labeling of a graph $$G$$ is an assignment of nonnegative integers to $$V(G)$$ such that the difference between labels of adjacent vertices is at least $$j,$$ and the difference between labels of vertices that are distance two apart is at least $$k.$$ The span of an $$L(j,k)$$ -labeling of a graph $$G$$ is the difference between the maximum and minimum integers used by it. The $$L(j,k)$$ -labelings-number of $$G$$ is the minimum span over all $$L(j,k)$$ -labelings of $$G.$$ This paper focuses on Nordhaus–Gaddum-type results for path covering and $$L(2,1)$$ -labeling numbers.

Suggested Citation

  • Damei Lü & Juan Du & Nianfeng Lin & Ke Zhang & Dan Yi, 2015. "Nordhaus–Gaddum-type results for path covering and $$L(2,1)$$ -labeling numbers," Journal of Combinatorial Optimization, Springer, vol. 29(2), pages 502-510, February.
    • Handle: RePEc:spr:jcomop:v:29:y:2015:i:2:d:10.1007_s10878-013-9610-3
    DOI: 10.1007/s10878-013-9610-3
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