is.triangulated             package:RBGL             R Documentation

_D_e_c_i_d_e _i_f _a _g_r_a_p_h _i_s _t_r_i_a_n_g_u_l_a_t_e_d

_D_e_s_c_r_i_p_t_i_o_n:

     Decide if a graph is triangulated

_U_s_a_g_e:

     is.triangulated(g)

_A_r_g_u_m_e_n_t_s:

       g: an instance of the 'graph' class 

_D_e_t_a_i_l_s:

     An undirected graph G = (V, E) is triangulated (i.e. chordal) if
     all cycles [v1, v2, ..., vk] of length 4 or more have a chord,
     i.e., an edge [vi, vj] with j != i +/- 1 (mod k)

     An equivalent definition of chordal graphs is:

     G is chordal iff either G is an empty graph, or there is an v in V
     such that

        1.  the neighborhood of v (i.e., v and its adjacent nodes)
           forms a clique, and

        2.  recursively, G-v is chordal

_V_a_l_u_e:

     The return value is 'TRUE' if 'g' is triangulated and 'FALSE'
     otherwise. An error is thrown if the graph is not  undirected; you
     might use 'ugraph' to compute the underlying  graph.

_A_u_t_h_o_r(_s):

     Li Long <li.long@isb-sib.ch>

_R_e_f_e_r_e_n_c_e_s:

     Combinatorial Optimization: algorithms and complexity  (p. 403) by
     C. H. Papadimitriou, K. Steiglitz

_S_e_e _A_l_s_o:

_E_x_a_m_p_l_e_s:

     coex <- fromGXL(file(system.file("XML/conn.gxl",package="RBGL"), open="r"))
     is.triangulated(coex)
     coex <- fromGXL(file(system.file("XML/hcs.gxl",package="RBGL"), open="r"))
     is.triangulated(coex)

