Geodesic
Polynomial solvability of the independent set problem for one class of graphs with small diameter
Diskretnyj analiz i issledovanie operacij, Tome 19 (2012) no. 4, pp. 66-72

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A constructive approach to forming new cases in the family of hereditary parts of the set ${\mathcal Free}(\{P_5,C_5\})$ with polynomial-time solvability of the independent set problem is considered. We prove that if this problem is polynomial-time solvable in the class ${\mathcal Free}(\{P_5,C_5,G\})$ then for any graph $H$ which can inductively be obtained from $G$ by means of applying addition with $K_1$ or multiplication by $K_1$ to the graph $G$ the problem has the same computational status in ${\mathcal Free}(\{P_5,C_5,H\})$. Bibliogr. 10.
Keywords: the independent set problem, computational complexity
Mots-clés : polynomial algorithm. 
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     author = {D. S. Malyshev},
     title = {Polynomial solvability of the independent set problem for one class of graphs with small diameter},
     journal = {Diskretnyj analiz i issledovanie operacij},
     pages = {66--72},
     publisher = {mathdoc},
     volume = {19},
     number = {4},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DA_2012_19_4_a5/}
}
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D. S. Malyshev. Polynomial solvability of the independent set problem for one class of graphs with small diameter. Diskretnyj analiz i issledovanie operacij, Tome 19 (2012) no. 4, pp. 66-72. http://geodesic.mathdoc.fr/item/DA_2012_19_4_a5/