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Edge-dominating cycles, k-walks and Hamilton prisms in 2K2-free graphs

Gao Mou, Dmitrii V. Pasechnik
2016 Journal of knot theory and its ramifications  
We show that an edge-dominating cycle in a 2K_2-free graph can be found in polynomial time; this implies that every 1/(k-1)-tough 2K_2-free graph admits a k-walk, and it can be found in polynomial time  ...  Furthermore, we prove that for any ϵ>0 every (1+ϵ)-tough 2K_2-free graph is prism-Hamiltonian and give an effective construction of a Hamiltonian cycle in the corresponding prism, along with few other  ...  The authors thank Nick Gravin and Edith Elkind for helpful comments on drafts of this text. Research supported by Singapore MOE Tier 2 Grant MOE2011-T2-1-090 (ARC 19/11).  ... 
doi:10.1142/s0218216516420116 fatcat:sg2cd7pz75ghbkb6sdunvomvve

2-walks in 2-tough 2k2-free graphs [article]

Gao Mou
2014 arXiv   pre-print
In this paper, we prove that in every 2-tough 2K_2-free graph, there is a 2-walk.  ...  Every 2-tough 2K 2 -free graph admits a 2-walk. On 2K 2 -free graphs We present several structural properties of 2K 2 -free graphs which turn out to be very useful in the proof of the main theorem.  ...  For some classes of graphs, there are strong results connected toughness and Hamiltonicity (recall that a 1-walk is a Hamiltonian cycle). E.g. in [2] , G. Chen, M.S. Jackson, A.E. Kezdy, and J.  ... 
arXiv:1408.3380v3 fatcat:pcrwqjzmfrcbhgron6iti3mfsy

Page 2132 of Mathematical Reviews Vol. , Issue 97D [page]

1997 Mathematical Reviews  
It is (also) applicable to the show- ing of the Hamiltonicity of K, 3-free graphs with low edge density and low degrees.” 97d:05200 05C45 Li, Mingchu (PRC-BST-MM; Beijing) Hamiltonian cycles in regular  ...  For example, the Ramsey number for any triple that contains any one of the graphs P;, 2K2, K,3, P4 is deter- mined. Ralph Faudree (1-MEMP; Memphis, TN)  ... 

Hamiltonicity of 3-tough (K_2 ∪ 3K_1)-free graphs [article]

Andrew Hatfield, Elizabeth Grimm
2021 arXiv   pre-print
We say that a graph is (K_2 ∪ 3K_1)-free if it contains no induced subgraph isomorphic to K_2 ∪ 3K_1, where K_2 ∪ 3K_1 is the disjoint union of an edge and three isolated vertices.  ...  In this paper, we show that every 3-tough (K_2 ∪ 3K_1)-free graph with at least three vertices is hamiltonian.  ...  Songling Shan for her guidance during the research process and her valuable feedback.  ... 
arXiv:2106.07083v1 fatcat:qpsfe2msivaxxfkyp6res7nswm

On the Physical Conditions Involved in the Construction of Artillery, and on Some Hitherto Unexplained Causes of the Destruction of Cannon in Service

Robert Mallet
1856 Transactions of the Royal Irish Academy  
of tenacity and toughness is demanded.  ...  I By order of the Committee, " Philadelphia, August 8, 1844." " WILLIAM HAMILTON, Actuary.  ...  of the gun was reduced, in a planing-machine, to the size of 2 inches square, and was subjected to a transverse strain, supported at both sides on knife-edges 20 inches apart, and the weight applied in  ... 

Analytical study of Carl Sandburg as poet and biographer

Mary Grace Ruszkowski, Université D'Ottawa / University Of Ottawa, Université D'Ottawa / University Of Ottawa
-"And So Today" The rhythms here are those of free verse.  ...  ., Americans, New York, Scribner & Sons, 1922, p. 2k2.  ...  Lowell, Amy, Poetry and Poets, New York, Houghton, Mifflin C 0 ., 1930, 232 pp. This is a series of critical essays on poetry of the elder poets and of contemporaries.  ... 
doi:10.20381/ruor-8896 fatcat:xzcb2ydoljhcnb64q6kdfmdqum

Cross-country food consumption patterns: theory and measurement [article]

Hai Yan Liu
On the basis of the multi-level budgeting system, we use a reverse-engineering approach to recover the unconditional demand equations that depend on income and the prices of all goods.  ...  demands, conditional on total food expenditure; and the food demand equation depending on income.  ...  On the other hand, beer and spirits are both independent of consumption of wine. As stated above, the matrix only 13 n in ij [ ] n is a free parameter.  ... 
doi:10.4225/23/5afa3793213fd fatcat:jbqkbg622ng7xjlm4wzlkyihpy