
Finding Efficient Domination for S_1,3,3Free Bipartite Graphs in Polynomial Time
A vertex set D in a finite undirected graph G is an efficient dominating...
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On the Bipartiteness Constant and Expansion of Cayley Graphs
Let G be a finite, undirected dregular graph and A(G) its normalized ad...
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FPRAS via MCMC where it mixes torpidly (and very little effort)
Is Fully Polynomialtime Randomized Approximation Scheme (FPRAS) for a p...
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Finding Dominating Induced Matchings in P_9Free Graphs in Polynomial Time
Let G=(V,E) be a finite undirected graph. An edge set E' ⊆ E is a domin...
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Openindependent, openlocatingdominating sets: structural aspects of some classes of graphs
Let G=(V(G),E(G)) be a finite simple undirected graph with vertex set V(...
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Strengthening some complexity results on toughness of graphs
Let t be a positive real number. A graph is called ttough if the remova...
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Map graphs having witnesses of large girth
A halfsquare of a bipartite graph B=(X,Y,E_B) has one color class of B ...
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Finding Efficient Domination for S_1,1,5Free Bipartite Graphs in Polynomial Time
A vertex set D in a finite undirected graph G is an efficient dominating set (e.d.s. for short) of G if every vertex of G is dominated by exactly one vertex of D. The Efficient Domination (ED) problem, which asks for the existence of an e.d.s. in G, is complete for various Hfree bipartite graphs, e.g., Lu and Tang showed that ED is complete for chordal bipartite graphs and for planar bipartite graphs; actually, ED is complete even for planar bipartite graphs with vertex degree at most 3 and girth at least g for every fixed g. Thus, ED is complete for K_1,4free bipartite graphs and for C_4free bipartite graphs. In this paper, we show that ED can be solved in polynomial time for S_1,1,5free bipartite graphs.
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