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Journal of Combinatorial Theory, Series B, 2018 Let $G=(V,E)$ be a graph and let $A_G$ be the clique-vertex incidence matrix of $G$. It is well known that $G$ is perfect iff the system $A_{_G}\mathbf x\le \mathbf 1$, $\mathbf x\ge\mathbf0$ is totally dual integral (TDI). In 1982, Cameron and Edmonds proposed to call $G$ box-perfect if the system $A_{_G}\mathbf x\le \mathbf 1$, $\mathbf x\ge\mathbf0$
Guoli Ding, Wenan Zang, Qiulan Zhao
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Perfectness of clustered graphs [PDF]
Discrete Optimization, 2013 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Flavia Bonomo +3 more
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An induced subgraph characterization of domination perfect graphs [PDF]
, 1995 Let γ(G) ι(G) be the domination number and independent domination number of a graph (G), respectively. A graph (G) is called domination perfect if γ(H) = ι(H), for every induced subgraph H of (G).
Vadim E. Zverovich +5 more
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Independent sets of maximum weight in apple-free graphs [PDF]
, 2010 We present the first polynomial-time algorithm to solve the maximum weight independent set problem for apple-free graphs, which is a common generalization of several important classes where the problem can be solved efficiently, such as claw-free graphs,
Lozin, Vadim V. +2 more
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Random Structures & Algorithms, 2018 We investigate the asymptotic structure of a random perfect graph Pn sampled uniformly from the set of perfect graphs on vertex set . Our approach is based on the result of Prömel and Steger that almost all perfect graphs are generalised split graphs, together with a method to generate such graphs almost uniformly.
McDiarmid, C, Yolov, N
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Line game-perfect graphs [PDF]
Discrete Mathematics & Theoretical Computer ScienceThe $[X,Y]$-edge colouring game is played with a set of $k$ colours on a graph $G$ with initially uncoloured edges by two players, Alice (A) and Bob (B). The players move alternately. Player $X\in\{A,B\}$ has the first move. $Y\in\{A,B,-\}$.
Stephan Dominique Andres, Wai Lam Fong
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Balancedness of subclasses of circular-arc graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 Graph ...
Flavia Bonomo +3 more
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The Forcing Domination Number of Hamiltonian Cubic Graphs [PDF]
, 2009 The authors presented a sequence of Hamiltonian cubic graphs whose domination numbers are sharp and in this paper we study forcing domination number for those ...
H. Abdollahzadeh Ahangar +3 more
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Perfect matching transitivity of circulant graphs.
Electronic Journal of Graph Theory and Applications, 2022 A graph G is perfect matching transitive, shortly PM-transitive, if for any two perfect matchings M1 and M2 of G, there is an automorphism f : V(G)↦V(G) such that fe(M1)=M2, where fe(uv)=f(u)f(v).
Isaac Armando Reiter, Ju Zhou
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Strongly perfect products of graphs [PDF]
, 1977 In this paper perfectness of various products of graphs is considered. The Cartesian product G1 × G2 is perfect iff it has no induced C2n+1 (n ⩾ 2). By considering the various sufficient conditions for the latter condition, perfect Cartesian products are
Parthasarathy, K.R. +3 more
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