- Adam N. Letchford added an answer:9How can I optimize a function on a Planar Graph?
- Vikant Bhateja added an answer:2How to apply combinatorial analysis in image fusion?
- Antonio Piccolomini d'Aragona added an answer:4Can someone help on an exercise on the consistency of the SKI calculus?
- Marcel Van de Vel added an answer:16Does the discrete n-circle (n even) admit a partition into n/2 pairs, all with a distinct diameter?
- David G Glynn added an answer:2Can we have any logical definition of infinite matroids and related defined codes?
- Yoshinori Shiozawa added an answer:4Do you know the number of all spanning trees of a given class?
- Sonam Kumar added an answer:12Can we use discrete mathematics in modeling of control and dynamical systems?
- Jean Moulin-Ollagnier added an answer:9Is there a bijective proof of : the rational number q_{m,n} = \frac {(2m)! (2n)!} {m! n! (m+n)!}, where m,n are positive integers, is an integer ?
- O.V.Shanmuga Sundaram added an answer:2Re: research
- SIMON RAJ F added an answer:14Is there any Barnette Graph with 2k (even number greater than 84) vertices?
- Krishnan Umachandran added an answer:7What are the applications of additive combinatorics in the field of engineering and architecture?
- Maimaiti Wulayimu added an answer:3Baker Hausdorff decoupling formula
- Miguel A. Pizaña added an answer:4What are the major real life or practical applications of intersection graphs?
- Sam W. Murphy added an answer:8Knapsack Packing Problem. Anyone have experience with this?
- Daniel Wright added an answer:6Just where do we draw the distinctive line between traditional data analysis and present day (Big) data analytics?
- Sudev Naduvath added an answer:10Where can I find useful literature on graph theoretical applications to biological networks?
- Marzieh Eini Keleshteri added an answer:2What can be said about the $q$-analogue of the Sheffer identity?
- Joe Mccollum added an answer:9What is the number of subsets of a finite set of non-negative integers which are neither the sumsets or the summands of other subsets of $X$?
- Natig Aliyev added an answer:9What are the graphs whose total graphs are complete graphs?
- Qefsere Doko Gjonbalaj added an answer:4How can we relate set theory with networks theory?
- Wiwat Wanicharpichat added an answer:6Can anybody suggest any references for combinatorial studies on perturbation theory?
- Tapas Chatterjee added an answer:8Is it right to take the sumset A + ∅ = ∅?
- Attila Por added an answer:18Is there any possibility for the sumset of two sets of integers, which are not arithmetic progressions, to be an arithmetic progression?
- Sanjib Kuila added an answer:4Why does the four colorability of planar graphs not ensure the non-biplanarity of K_9?
- Sudev Naduvath added an answer:4Compute the number of path from a node to a different one in a weighted undirected connected 3-regular graph.
- Sudev Naduvath added an answer:3Are there any specific studies on the maximal bipartite sub-graphs of different products of two regular graphs?
- Mihai Prunescu added an answer:4Where can I find some real life or scientific applications of the sumsets of two sets of real numbers?
- Patrick Solé added an answer:1Is it possible to find an infinite arithmetic progression of value of k such that we can get primes of the form 6k+1 successively?
- Paolo Leonetti added an answer:3How to decrease the bounded gaps between primes?

#### About Combinatorics

Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size (enumerative combinatorics), deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria (as in combinatorial designs and matroid theory), finding "largest", "smallest", or "optimal" objects (extremal combinatorics and combinatorial optimization), and studying combinatorial structures arising in an algebraic context, or applying algebraic techniques to combinatorial problems (algebraic combinatorics).

Assuming we have a planar Graph G=(V,E). There is a function f(G) which returns a positive real number and we wish to assign either 0 or 1 to each node in order to minimize the function f(G). Trying all different combinations of assigning 0 or 1 to each node to find the combination which returns the minimum value of f(G) would be computational intractable. Hence, the question is whether there exists a algorithm to find (or approximate) the minimum for such a function.

Note that the function f has the properties that a solution exists and is unique. Further, it is known that the Graph that minimizes the function has 0 in the vast majority of nodes and the set where the nodes are 1 is connected.