Approximate graph products

The problem of recognizing approximate graph products arises in theoretical biology. This paper presents an algorithm that recognizes a large class of approximate graph products. The main part of this contribution is concerned with a new, local prime factorization algorithm that factorizes all strong products on an extensive class of graphs that contains, in particular, all products of triangle-free graphs on at least three vertices. The local approach is linear for graph with fixed maximal degree.

[1]  Wilfried Imrich,et al.  Recognizing Cartesian products in linear time , 2007, Discret. Math..

[2]  P. Schuster,et al.  IR-98-039 / April Continuity in Evolution : On the Nature of Transitions , 1998 .

[3]  Peter F. Stadler,et al.  The Topology of Evolutionary Biology , 2004 .

[4]  Stephan Kopp,et al.  RNA Shape Space Topology , 1999, Artificial Life.

[5]  J. Schiff Wiley‐Interscience Series in Discrete Mathematics and Optimization , 2011 .

[6]  Joan Feigenbaum,et al.  Finding the prime factors of strong direct product graphs in polynomial time , 1992, Discret. Math..

[7]  H. Crichton-Miller Adaptation , 1926 .

[8]  G. Wagner,et al.  The topology of the possible: formal spaces underlying patterns of evolutionary change. , 2001, Journal of theoretical biology.

[9]  V. G. Vizing The cartesian product of graphs , 1963 .

[10]  Joan Feigenbaum,et al.  A polynomial time algorithm for finding the prime factors of cartesian-product graphs , 1985, Discret. Appl. Math..

[11]  Joan Feigenbaum,et al.  On Factorable Extensions and Subgraphs of Prime Graphs , 1989, SIAM J. Discret. Math..

[12]  P. Schuster,et al.  Shaping space: the possible and the attainable in RNA genotype-phenotype mapping. , 1998, Journal of theoretical biology.

[13]  Peter F Stadler,et al.  Quasi-independence, homology and the unity of type: a topological theory of characters. , 2003, Journal of theoretical biology.

[14]  Gert Sabidussi,et al.  Graph multiplication , 1959 .

[15]  Ralph McKenzie,et al.  Cardinal multiplication of structures with a reflexive relation , 1971 .