论文信息 - A note on the complexity of finding regular subgraphs

A note on the complexity of finding regular subgraphs

Given a graph G and an integer r, does there exist a regular subgraph of G with degree r? In this note we establish NP-completeness for the r-regular subgraph problem for each r >= 3 and certain restrictions on G. In particular, the cubic subgraph problem is NP-complete even for the simple case where G is a bipartite planar graph with maximum degree 4.

Ján Plesník | J. Plesník

[1] V. Sós,et al. On a problem of K. Zarankiewicz , 1954 .

[2] J. A. Bondy,et al. Graph Theory with Applications , 1978 .

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

[4] Frank Harary,et al. Graph Theory , 2016 .

[5] Carsten Thomassen,et al. Three-regular subgraphs of four-regular graphs , 1979, J. Graph Theory.

[6] J. A. Bondy,et al. Graph Theory with Applications , 1978 .

[7] P. Erdős,et al. COLLOQUIA MATHEMATICA SOCIETATIS JÁNOS BOLYAI 4 . COMBINATORIAL THEORY AND ITS APPLICATIONS , 1969 .

[8] K. Parthasarathy,et al. On the (4–3)-regular subgraph conjecture , 1981 .

[9] K. R. Parthasarathy,et al. On the berge - sauer conjecture , 1982, J. Graph Theory.