Yazar "Civan, Yusuf" seçeneğine göre listele

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    Bounding the chromatic number of squares of K-4-minor-free graphs
    (Elsevier Science Bv, 2019) Civan, Yusuf; Deniz, Zakir; Yetim, Mehmet Akif
    Let G be a K-4-minor-free graph with Delta(G) >= 3. We prove that if G contains no subgraph isomorphic to K-2(,r) for some r >= 1. then chi(G(2)) <= Delta(G) + r. (C) 2019 Elsevier B.V. All rights reserved.
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    Domination versus edge domination on claw-free graphs
    (Elsevier, 2023) Civan, Yusuf; Deniz, Zakir; Yetim, Mehmet Akif
    When G is a (finite and simple) graph, we prove that its domination number is at most its edge-domination number if G is a claw-free graph with minimum degree at least two. That generalizes an earlier result of Baste et al. (2020) on cubic claw-free graphs.(c) 2023 Elsevier B.V. All rights reserved.
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    Gated independence in graphs
    (Elsevier, 2024) Civan, Yusuf; Deniz, Zakir; Yetim, Mehmet Akif
    If G = ( V , E ) is a (finite and simple) graph, we call an independent set X a gated independent set in G if for each x is an element of X , there exists a neighbor y of x such that ( X \ { x } ) boolean OR{ y } is an independent set in G . We define the gated independence number gi( G ) of G to be the maximum cardinality of a gated independent set in G . We demonstrate that the gated independence number is closely related to both matching and domination parameters of graphs. We prove that the inequalities im( G ) gi( G ) m ur ( G ) hold for every graph G , where im( G ) and m ur ( G ) denote the induced and uniquely restricted matching numbers of G . On the other hand, we show that gamma i ( G ) gi( G ) and gamma p r ( G ) 2 gi( G ) for every graph G without any isolated vertex, where gamma i ( G ) and gamma p r ( G ) denote the independence and paired domination numbers. Furthermore, we provide bounds on the gated independence number involving the order, size and maximum degree. In particular, we prove that gi( G ) 5 n for every n -vertex subcubic graph G without any isolated vertex or any component isomorphic to K 3 , 3 , and gi( B ) 3 n 8 for every n -vertex connected cubic bipartite graph B . (c) 2024 Elsevier B.V. All rights reserved.
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    Order-Sensitive Domination in Partially Ordered Sets and Graphs
    (Springer, 2022) Civan, Yusuf; Deniz, Zakir; Yetim, Mehmet Akif
    For a (finite) partially ordered set (poset) P, we call a dominating set D in the comparability graph of P, an order-sensitive dominating set in P if either x is an element of D or else a < x < b in P for some a,b is an element of D for every element x in P which is neither maximal nor minimal, and denote by gamma(os)(P), the least size of an order-sensitive dominating set of P. For every graph G and integer k >= 2, we associate to G a graded poset P-k(G) of height k, and prove that gamma(os)(P-3(G)) = gamma(R)(G) and gamma(os)(P-4(G)) = 2 gamma(G) hold, where gamma(G) and gamma(R)(G) are the domination and Roman domination number of G respectively. Moreover, we show that the order-sensitive domination number of a poset P exactly corresponds to the biclique vertex-partition number of the associated bipartite transformation of P.