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Journal of Combinatorial Theory, Series B, 1973 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Norman Biggs
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Square-free perfect graphs [PDF]
Journal of Combinatorial Theory, Series B, 2003 We prove that square-free perfect graphs are bipartite graphs or line graphs of bipartite graphs or have a 2-join or a star cutset.
Michele Conforti +2 more
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On co-maximal subgroup graph of $Z_n$ [PDF]
International Journal of Group Theory, 2022 The co-maximal subgroup graph $\Gamma(G)$ of a group $G$ is a graph whose vertices are non-trivial proper subgroups of $G$ and two vertices $H$ and $K$ are adjacent if $HK = G$.
Manideepa Saha +2 more
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Total perfect codes in graphs realized by commutative rings [PDF]
Transactions on Combinatorics, 2022 Let $R$ be a commutative ring with unity not equal to zero and let $\Gamma(R)$ be a zero-divisor graph realized by $R$. For a simple, undirected, connected graph $G = (V, E)$, a {\it total perfect code} denoted by $C(G)$ in $G$ is a subset $C(G ...
Rameez Raja
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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 $A_{_G}\mathbf x\le \mathbf 1$, $\mathbf x\ge\mathbf0$
Zang, W, ZHAO, Q, Ding, G
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Fractional matching preclusion for generalized augmented cubes [PDF]
Discrete Mathematics & Theoretical Computer Science, 2019 The \emph{matching preclusion number} of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost perfect matchings.
Tianlong Ma +3 more
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On two consequences of Berge–Fulkerson conjecture
AKCE International Journal of Graphs and Combinatorics, 2020 The classical Berge–Fulkerson conjecture states that any bridgeless cubic graph admits a list of six perfect matchings such that each edge of belongs to two of the perfect matchings from the list.
Vahan V. Mkrtchyan, Gagik N. Vardanyan
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Parameters of the coprime graph of a group [PDF]
International Journal of Group Theory, 2021 There are many different graphs one can associate to a group. Some examples are the well-known Cayley graph, the zero divisor graph (of a ring), the power graph, and the recently introduced coprime graph of a group.
Jessie Hamm, Alan Way
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Complementation in T-perfect Graphs [PDF]
, 2021 Inspired by applications of perfect graphs in combinatorial optimization, Chv tal defined t-perfect graphs in 1970s. The long efforts of characterizing t-perfect graphs started immediately, but embarrassingly, even a working conjecture on it is still missing after nearly 50 years.
Yixin Cao, Shenghua Wang
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Two short proofs of the Perfect Forest Theorem
Theory and Applications of Graphs, 2017 A perfect forest is a spanning forest of a connected graph $G$, all of whose components are induced subgraphs of $G$ and such that all vertices have odd degree in the forest.
Yair Caro, Josef Lauri, Christina Zarb
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