论文信息 - Finding Regular Subgraphs in Both Arbitrary and Planar Graphs

Finding Regular Subgraphs in Both Arbitrary and Planar Graphs

Abstract We show that the problems of deciding (i) whether an arbitrary graph has a k-regular subgraph, for some given k ⩾ 3, (ii) whether a planar graph has a quartic subgraph, and (iii) whether a planar graph has a quintic subgraph, are complete for NP via logspace reductions. There are no regular planar graphs of degree greater than 5.

Iain A. Stewart

[1] N. Biggs. Algebraic Graph Theory: The multiplicative expansion , 1974 .

[2] Martenc Jones Colbourn. Algorithmic Aspects of Combinatorial Designs: A Survey , 1985 .

[3] David S. Johnson,et al. Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[4] Stephen A. Cook,et al. Problems Complete for Deterministic Logarithmic Space , 1987, J. Algorithms.

[5] Iain A. Stewart. Deciding whether a planar graph has a cubic subgraph is NP-complete , 1994, Discret. Math..

[6] Jan van Leeuwen,et al. Graph Algorithms , 1991, Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity.

[7] Claude Berge,et al. Graphs and Hypergraphs , 2021, Clustering.

[8] Charles J. Colbourn,et al. Applications of combinatorial designs in computer science , 1989, CSUR.

[9] Iain A. Stewart. On locating cubic subgraphs in bounded-degree connected bipartite graphs , 1997, Discret. Math..

[10] J. Van Leeuwen,et al. Handbook of theoretical computer science - Part A: Algorithms and complexity; Part B: Formal models and semantics , 1990 .