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/* Copyright (c) 1997-2024
Ewgenij Gawrilow, Michael Joswig, and the polymake team
Technische Universität Berlin, Germany
https://polymake.org
This program is free software; you can redistribute it and/or modify it
under the terms of the GNU General Public License as published by the
Free Software Foundation; either version 2, or (at your option) any
later version: http://www.gnu.org/licenses/gpl.txt.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
--------------------------------------------------------------------------------
*/
#pragma once
#include "polymake/GenericGraph.h"
#include "polymake/vector"
#include "polymake/list"
#include "polymake/Set.h"
#include "polymake/Vector.h"
namespace polymake { namespace graph {
/* Determine whether an undirected graph is bipartite.
* Returns a negative Int if not bipartite. If the graph is bipartite,
* the absolute difference of the black and white colored nodes is returned.
* Also works for disconnected graphs (albeit its use may be limited).
*
* @author Niko Witte
*/
template <typename Graph>
Int bipartite_sign(const GenericGraph<Graph, Undirected>& G);
// given a bipartite graph, color it with two colors, 0 and 1
template <typename Graph>
Vector<Int> bipartite_coloring(const GenericGraph<Graph,Undirected>& G)
{
assert(G.nodes() > 0);
Vector<Int> color_of(G.nodes(), 2); // initialize to dummy color 2
std::list<Int> queue;
queue.push_back(0);
color_of[0] = 1;
Set<Int> new_nodes(sequence(0, G.nodes()));
while (queue.size()) {
const Int n = queue.front(); queue.pop_front();
new_nodes -= n;
const Set<Int> neighbors = G.top().adjacent_nodes(n) * new_nodes;
const bool color = color_of[n];
for (auto sit = entire(neighbors); !sit.at_end(); ++sit) {
queue.push_back(*sit);
if (color_of[*sit] != 2 && color_of[*sit] != !color)
throw std::runtime_error("Graph is not bipartite");
color_of[*sit] = !color;
}
}
return color_of;
}
} }
#include "polymake/graph/bipartite.tcc"
// Local Variables:
// mode:C++
// c-basic-offset:3
// indent-tabs-mode:nil
// End:
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