Results 21 to 30 of about 116,736 (298)

Planar anti-Ramsey numbers of paths and cycles [PDF]

Discrete Mathematics, 2017
Motivated by anti-Ramsey numbers introduced by Erd\H{o}s, Simonovits and S\'os in 1975, we study the anti-Ramsey problem when host graphs are plane triangulations.
Yongxin Lan, Yongtang Shi, Zi-Xia Song
semanticscholar   +1 more source

On Hamiltonian Paths and Cycles in Sufficiently Large Distance Graphs [PDF]

Discrete Mathematics & Theoretical Computer Science, 2014
Graph ...
Christian Löwenstein, Dieter Rautenbach, Roman Soták   +2 more
doaj   +1 more source

Long monochromatic paths and cycles in 2-edge-colored multipartite graphs [PDF]

Moscow Journal of Combinatorics and Number Theory, 2019
We solve four similar problems: For every fixed $s$ and large $n$, we describe all values of $n_1,\ldots,n_s$ such that for every $2$-edge-coloring of the complete $s$-partite graph $K_{n_1,\ldots,n_s}$ there exists a monochromatic (i) cycle $C_{2n ...
J. Balogh, A. Kostochka, Mikhail Lavrov, Xujun Liu   +3 more
semanticscholar   +1 more source

Noncrossing Longest Paths and Cycles [PDF]

Graphs and Combinatorics
Edge crossings in geometric graphs are sometimes undesirable as they could lead to unwanted situations such as collisions in motion planning and inconsistency in VLSI layout.
G. Aloupis, Ahmad Biniaz, Prosenjit Bose, J. De Carufel, D. Eppstein, Anil Maheshwari, Saeed Odak, M. Smid, Csaba D. Tóth, Pavel Valtr   +9 more
semanticscholar   +1 more source

Generalized paths and cycles in semicomplete multipartite digraphs [PDF]

Discrete Applied Mathematics
It is well-known and easy to show that even the following version of the directed travelling salesman problem is NP-complete: Given a strongly connected complete digraph $D=(V,A)$, a cost function $w: A\rightarrow \{0,1\}$ and a natural number $K ...
J. Bang-Jensen, Yun Wang, Anders Yeo
semanticscholar   +1 more source

Optimal Identifying Codes in Cycles and Paths [PDF]

, 2022
The concept of identifying codes in a graph was introduced by Karpovsky et al. (in IEEE Trans Inf Theory 44(2):599-611, 1998). These codes have been studied in several types of graphs such as hypercubes, trees, the square grid, the triangular grid ...
Laihonen T, Junnila V
core   +1 more source

Connected domination game played on Cartesian products

Open Mathematics, 2019
The connected domination game on a graph G is played by Dominator and Staller according to the rules of the standard domination game with the additional requirement that at each stage of the game the selected vertices induce a connected subgraph of G. If
Bujtás Csilla, Dokyeesun Pakanun, Iršič Vesna, Klavžar Sandi   +3 more
doaj   +1 more source

Intersecting longest paths and longest cycles: A survey

Electronic Journal of Graph Theory and Applications, 2013
This is a survey of results obtained during the last 45 years regarding the intersection behaviour of all longest paths, or all longest cycles, in connected graphs. Planar graphs and graphs of higher connectivity receive special attention.
Ayesha Shabbir, Carol T. Zamfirescu, Tudor I. Zamfirescu   +2 more
doaj   +1 more source

Partitioning 2-edge-colored graphs by monochromatic paths and cycles [PDF]

Comb., 2014
We present results on partitioning the vertices of 2-edge-colored graphs into monochromatic paths and cycles. We prove asymptotically the two-color case of a conjecture of Sárközy: the vertex set of every 2-edge-colored graph can be partitioned into at ...
J. Balogh, J. Barát, Dániel Gerbner, A. Gyárfás, G. N. Sárközy   +4 more
semanticscholar   +1 more source

Cycles and Paths Related Vertex-Equitable Graphs

Journal of Combinatorial Mathematics and Combinatorial Computing, 2023
A vertex labeling \(\xi\) of a graph \(\chi\) is referred to as a 'vertex equitable labeling (VEq.)' if the induced edge weights, obtained by summing the labels of the end vertices, satisfy the following condition: the absolute difference in the number ...
S. Nazeer, Najma Sultana, E. Bonyah
semanticscholar   +1 more source