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Journal of Combinatorial Theory, Series B, 2023
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Sergey Norin +2 more
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Sergey Norin +2 more
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Combinatorics, Probability and Computing, 1996
In this paper, we prove that every graph contains a cycle intersecting all maximum independent sets. Using this, we further prove that every graph with stability number α is spanned by α disjoint cycles. Here, the empty set, the graph of order 1 and the path of order 2 are all considered as degenerate cycles.
Chen, C.C., Jin, G.P.
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In this paper, we prove that every graph contains a cycle intersecting all maximum independent sets. Using this, we further prove that every graph with stability number α is spanned by α disjoint cycles. Here, the empty set, the graph of order 1 and the path of order 2 are all considered as degenerate cycles.
Chen, C.C., Jin, G.P.
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Cycles and Connectivity in Graphs
Canadian Journal of Mathematics, 1967In this note, G will denote a finite undirected graph without multiple edges, and V = V(G) will denote its vertex set. The largest integer n for which G is n-vertex connected is the vertex-connectivity of G and will be denoted by λ = λ(G). One defines ζ to be the largest integer z not exceeding |V| such that for any set U ⊂ V with |U| = z, there is a ...
Watkins, M. E., Mesner, D. M.
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SIAM Journal on Discrete Mathematics, 1992
Let \(G\) be a bridgeless graph with \(n\) vertices and \(m\) edges and let \(r\) be the minimum length of an even cycle in \(G\) of length at least 6 \((r=\infty\) if there is no such cycle). It is proved that the edges of \(G\) can be covered by cycles whose total length is at most \(m+(n-1)r/(r- 1)\).
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Let \(G\) be a bridgeless graph with \(n\) vertices and \(m\) edges and let \(r\) be the minimum length of an even cycle in \(G\) of length at least 6 \((r=\infty\) if there is no such cycle). It is proved that the edges of \(G\) can be covered by cycles whose total length is at most \(m+(n-1)r/(r- 1)\).
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Networks, 2000
Summary: Three problems in connection with cycles on the butterfly graphs are studied in this paper. The first problem is to construct complete uniform cycle partitions for the butterfly graphs. Suppose that \(G= (V,E)\) is a graph. A partition \(\{V_1, V_2,\dots, V_s\}\) of \(V\) is said to be a uniform cycle partition of \(G\) if \(|V_1|= |V_2 ...
Shien-Ching Hwang, Gen-Huey Chen
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Summary: Three problems in connection with cycles on the butterfly graphs are studied in this paper. The first problem is to construct complete uniform cycle partitions for the butterfly graphs. Suppose that \(G= (V,E)\) is a graph. A partition \(\{V_1, V_2,\dots, V_s\}\) of \(V\) is said to be a uniform cycle partition of \(G\) if \(|V_1|= |V_2 ...
Shien-Ching Hwang, Gen-Huey Chen
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Computers & Operations Research, 1998
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Martine Labbé +2 more
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Martine Labbé +2 more
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ACM SIGCSE Bulletin, 2006
Most of the previous challenges in this column were based on very little CS knowledge, but required problem-solving competence. This is also the case with the "Queens on a chessboard" challenge solved in the second part of this issue. The first part of the issue presents a graph-based challenge and requires familiarity with graph algorithms.
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Most of the previous challenges in this column were based on very little CS knowledge, but required problem-solving competence. This is also the case with the "Queens on a chessboard" challenge solved in the second part of this issue. The first part of the issue presents a graph-based challenge and requires familiarity with graph algorithms.
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Combinatorica, 1991
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J. Adrian Bondy, Genghua Fan
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J. Adrian Bondy, Genghua Fan
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Distinguishing graphs via cycles
Discrete Applied Mathematics, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Nina Klobas, Matjaz Krnc
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