On the computational complexity of partial covers of Theta graphs

By use of elementary geometric arguments we prove the existence of a special integral solution of a certain system of linear equations. The existence of such a solution then yields the NP-hardness of the decision problem on the existence of locally injective homomorphisms to Theta graphs with three distinct odd path lengths.

[1]  Jan Kratochvíl,et al.  Coloring precolored perfect graphs , 1997 .

[2]  N. Biggs.  Algebraic Graph Theory , 1974 .

[3]  Martin G. Everett,et al.  Role colouring a graph , 1991 .

[4]  Michael R. Fellows,et al.  On the complexity and combinatorics of covering finite complexes , 1991, Australas. J Comb..

[5]  Jan Kratochvíl,et al.  Covering Regular Graphs , 1997, J. Comb. Theory B.

[6]  Jerrold R. Griggs,et al.  Labelling Graphs with a Condition at Distance 2 , 1992, SIAM J. Discret. Math..

[7]  Jan Kratochvíl,et al.  On the Complexity of Graph Covering Problems , 1994, Nord. J. Comput..

[8]  Jan Kratochvíl,et al.  Fixed-parameter complexity of lambda-labelings , 2001, Discret. Appl. Math..

[9]  Jirí Fiala.  NP completeness of the edge precoloring extension problem on bipartite graphs , 2003, J. Graph Theory.

[10]  J. V. D. Heuvel,et al.  Graph labeling and radio channel assignment , 1998 .

[11]  Ran Libeskind-Hadas,et al.  On Multicast Algorithms for Heterogeneous Networks of Workstations , 1989, J. Parallel Distributed Comput..

[12]  Jaroslav Nesetril,et al.  On the complexity of H-coloring , 1990, J. Comb. Theory, Ser. B.

[13]  Jirí Fiala,et al.  The Computational Complexity of the Role Assignment Problem , 2003, ICALP.

[14]  Jirí Fiala,et al.  Partial covers of graphs , 2002, Discuss. Math. Graph Theory.

[15]  Ian Holyer,et al.  The NP-Completeness of Edge-Coloring , 1981, SIAM J. Comput..

[16]  Jan Kratochvíl,et al.  Coloring precolored perfect graphs , 1997, J. Graph Theory.

[17]  Jaroslav Nesetril,et al.  Graphs and homomorphisms , 2004, Oxford lecture series in mathematics and its applications.

[18]  Jan Arne Telle,et al.  Generalized H-Coloring of Graphs , 2000, ISAAC.

[19]  Hans L. Bodlaender,et al.  The Classification of Coverings of Processor Networks , 1989, J. Parallel Distributed Comput..

[20]  Jan Kratochvíl,et al.  Complexity of Colored Graph Covers I. Colored Directed Multigraphs , 1997, WG.

[21]  Gary MacGillivray,et al.  On the complexity of H-colouring planar graphs , 2009, Discret. Math..

[22]  Jirí Fiala,et al.  Complexity of Partial Covers of Graphs , 2001, ISAAC.