A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Uniform coverings of 2-paths with 5-paths in the complete graph

2005
*
Discrete Mathematics
*

There exists a

doi:10.1016/j.disc.2004.03.019
fatcat:lpus6fbi4rhsvem23qzg7vpzwi
*uniform**covering**of**2*-*paths**with**5*-*paths**in*K n if and only if n is even or n ≡ 1 (mod 8). ... Acknowledgements*The*authors thank*the*referees for their valuable comments. References ... There exists a*uniform**covering**of**2*-*paths**with**5*-*paths**in*K n . Let k 1. From Propositions 2.1 and 2.2, there exist*uniform**coverings**of**2*-*paths**with**5*-*paths**in*K 8k and K 9 . ...##
###
Vertex covers by monochromatic pieces — A survey of results and problems

2016
*
Discrete Mathematics
*

This survey is devoted to problems and results concerning

doi:10.1016/j.disc.2015.07.007
fatcat:sssibblukngrxhnxjeeiut5rfy
*covering**the*vertices*of*edge colored*graphs*or hypergraphs*with*monochromatic*paths*, cycles and other objects. ... It is an expanded version*of**the*talk*with**the*same title at*the*Seventh Cracow Conference on*Graph*Theory, held*in*Rytro*in*September 14-19, 2014. ... Thanks for Gábor Sárközy for his remarks on*the*manuscript.*The*author is also indebted to referees for valuable remarks. ...##
###
Monochromatic Path and Cycle Partitions in Hypergraphs

2013
*
Electronic Journal of Combinatorics
*

Also, apart from $2k-

doi:10.37236/2631
fatcat:hmm5ntcssrebrl5frgc5vugz54
*5*$ vertices, $*2*$-colored $k$-*uniform*hypergraphs can be partitioned into two monochromatic loose paths.In general, we prove that*in*any $r$-coloring*of*a $k$-*uniform*hypergraph there ... Here we address*the*problem to partition edge colored hypergraphs by monochromatic*paths*and cycles generalizing a well-known similar problem for graphs.We show that $r$-colored $r$-*uniform**complete*hypergraphs ...*In*any*2*-coloring*of**the*edges*of*a finite*complete**graph**the*vertices can be partitioned into a red and a blue*path*. Here*the*empty*graph*and*the*one-vertex*graph*is accepted as a*path**of*any color. ...##
###
Monochromatic loose path partitions in k-uniform hypergraphs
[article]

2016
*
arXiv
*
pre-print

A conjecture

arXiv:1611.03259v1
fatcat:vmqxhlickre5rgalzrwy5r5uw4
*of*Gyárfás and Sárközy says that*in*every*2*-coloring*of**the*edges*of**the**complete*k-*uniform*hypergraph K_n^k, there are two disjoint monochromatic loose*paths**of*distinct colors such that ... A weaker form*of*this conjecture*with*2k-*5*uncovered vertices instead*of*k-*2*is proved, thus*the*conjecture holds for k=3. ... Proposition 1.1*In*any*2*-coloring*of**the*edges*of*a finite*complete**graph**the*vertices can be partitioned into a red and a blue*path*. ...##
###
Monochromatic paths in 2-edge coloured graphs and hypergraphs
[article]

2022
*
arXiv
*
pre-print

Further, we give a lower bound for

arXiv:2204.12464v1
fatcat:wyiy5koju5e45ndvm4qmanl34u
*the*number*of*tight*paths*needed to partition any*2*-edge-coloured*complete*k-partite k-*uniform*hypergraph, and show that any*2*-edge coloured bipartite*graph*has a partition ... We answer a question*of*Gyárfás and Sárközy from 2013 by showing that every*2*-edge-coloured*complete*3-*uniform*hypergraph can be partitioned into two monochromatic tight*paths**of*different colours. ... A variant*of**the*original problem*in**graphs*replaces*the*underlying*complete**graph**with**the**complete*balanced bipartite*graph*K n,n . ...##
###
On Hamiltonian Berge cycles in 3-uniform hypergraphs
[article]

2020
*
arXiv
*
pre-print

Given a set R, a hypergraph is R-

arXiv:1901.06042v3
fatcat:l6g7xzsluzdsdkd4ohub32ojwe
*uniform*if*the*size*of*every hyperedge belongs to R. A hypergraph H is called*covering*if every vertex pair is contained*in*some hyperedge*in*H. ... As an application, we determine*the*maximum Lagrangian*of*k-*uniform*Berge-C_t-free hypergraphs and Berge-P_t-free hypergraphs. ... This*completes**the*proof*of*Theorem 7. Proof*of*Corollary 9 and 10. For k = 3, Corollary 9 and 10 follows from Theorem 4 and Lemma 19 using*the*same logic as*the*proof*of*Theorem 7. ...##
###
Page 8951 of Mathematical Reviews Vol. , Issue 2003m
[page]

2003
*
Mathematical Reviews
*

-EDD; Shibuya)

*Uniform**coverings**of**2*-*paths**with**5*-*paths**in*K>,,. ... Summary: “We give a construction*of*a*uniform**covering**of**2*-*paths**with**5*-*paths**in*K,, for all even n > 6, i.e., we construct a set S*of**5*-*paths**in*K,, having*the*property that each*2*-*path**in*K,, lies ...##
###
Labeling, Covering And Decomposing Of Graphs — Smarandache'S Notion In Graph Theory

2010
*
Zenodo
*

This paper surveys

doi:10.5281/zenodo.9258
fatcat:rqsysf4dqreslozhxbiljqfbrm
*the*applications*of*Smarandache's notion to*graph*theory appeared*in*International J.Math.Combin. from Vol.1,2008 to Vol.3,2009. ...*In*fact, many problems discussed*in*these papers are generalized*in*this paper. ... my monograph*Graph*Theory -A Smarandachely Type will be appeared*in*2012. ...##
###
Labeling, Covering And Decomposing Of Graphs — Smarandache'S Notion In Graph Theory

2010
*
Zenodo
*

This paper surveys

doi:10.5281/zenodo.823874
fatcat:mzzws7nuijb33norbr5ifpzgh4
*the*applications*of*Smarandache's notion to*graph*theory appeared*in*International J.Math.Combin. from Vol.1,2008 to Vol.3,2009. ...*In*fact, many problems discussed*in*these papers are generalized*in*this paper. ... my monograph*Graph*Theory -A Smarandachely Type will be appeared*in*2012. ...##
###
Page 3572 of Mathematical Reviews Vol. , Issue 83i
[page]

1983
*
Mathematical Reviews
*

*The*

*graph*is then

*of*type (r-K,.--+

*2*),3

*in*other words, there are rc—c+

*2*classes

*with*r vertices,

*the*

*graph*induced by two classes is a matching, and between two vertices at distance

*2*, there are c

*paths*... Jung (Berlin) Kohler, Norbert 83i:05052 On

*path*-

*coverings*and Hamilton-connectivity

*of*finite

*graphs*. Arch. Math. ( Basel) 36 (1981), no.

*5*, 470-473. ...

##
###
Searching symmetric networks with Utilitarian-Postman paths

2009
*
Networks
*

We then show that if Q is symmetric

doi:10.1002/net.20314
fatcat:m4hvsrkfgnhoxmvkg6pde3vpca
*of*odd degree,*with*n vertices and m unit length edges,*the*value V*of*(Q) satis...es V m*2*+ n*2*2n 8m ;*with*equality if and only if Q has a*path*v 1 ; v*2*; : : : ... For any network Q; one may consider*the*zero-sum search game (Q)*in*which*the*(minimizing) Searcher picks a unit speed*path*S (t)*in*Q;*the*Hider picks a point H*in*Q; and*the*payo¤ is*the*meeting time ...*In*particular, all*complete**graphs*,*complete*bipartite*graphs*, hypercube*graphs*,*graphs**of*large valency, are HHHC. And yes,*the*Petersen*graph*is HHHC. ...##
###
Almost partitioning 2-coloured complete 3-uniform hypergraphs into two monochromatic tight or loose cycles
[article]

2018
*
arXiv
*
pre-print

We show that for every η > 0 there exists an integer n_0 such that every

arXiv:1701.07806v2
fatcat:wcqrmb6uyrcmtju53a6bztgxxu
*2*-colouring*of**the*3-*uniform**complete*hypergraph on n ≥ n_0 vertices contains two disjoint monochromatic tight cycles*of*distinct ...*The*same result holds if we replace tight cycles*with*loose cycles. ... It states that for every n, every*2*-colouring*of**the*edges*of**the**complete**graph*K n admits a*covering**of**the*vertices*of*K n*with*at most two monochromatic vertex disjoint cycles*of*different colours. ...##
###
Finding paths with minimum shared edges

2012
*
Journal of combinatorial optimization
*

to t

doi:10.1007/s10878-012-9462-2
fatcat:7szvmvpqkrh5ffgpmysivmqswi
*in*G so as to minimize*the*number*of*edges shared among*the**paths*. ... Motivated by a security problem*in*geographic information systems, we study*the*following*graph*theoretical problem: given a*graph*G, two special nodes s and t*in*G, and a number k, find k*paths*from s ... We used High Performance Computing Virtual Laboratory (HPCVL)'s Beowulf Cluster 3 that has 64 nodes*of*4×2.2 GHz Opteron Cores*with*8 GB RAM for running*the*experiments*in*parallel. ...##
###
Finding Paths with Minimum Shared Edges
[chapter]

2011
*
Lecture Notes in Computer Science
*

to t

doi:10.1007/978-3-642-22685-4_49
fatcat:4h5fktr2cbba3clvfqx57mebym
*in*G so as to minimize*the*number*of*edges shared among*the**paths*. ... Motivated by a security problem*in*geographic information systems, we study*the*following*graph*theoretical problem: given a*graph*G, two special nodes s and t*in*G, and a number k, find k*paths*from s ... We used High Performance Computing Virtual Laboratory (HPCVL)'s Beowulf Cluster 3 that has 64 nodes*of*4×2.2 GHz Opteron Cores*with*8 GB RAM for running*the*experiments*in*parallel. ...##
###
Partial barrier coverage: Using game theory to optimize probability of undetected intrusion in polygonal environments

2008
*
2008 IEEE International Conference on Robotics and Automation
*

We use ideas from noncooperative game theory together

doi:10.1109/robot.2008.4543615
dblp:conf/icra/KloderH08
fatcat:6ya5vg2yyvdmdotr64npqcswjq
*with*previous results from*complete*barrier coverage -*the*problem*of**completely*preventing undetected intrusion -to develop new methods that solve ...*In*this paper, we formalize*the*problem*of*partial barrier coverage, that is,*the*problem*of*using robot sensors (guards) to minimize*the*probability*of*undetected intrusion*in*a particular region by an ... A*complete*barrier*covers*all intrusion*paths*. A partial barrier*covers*an infinite set*of**paths*, and misses an infinite set*of**paths*. ...
« Previous

*Showing results 1 — 15 out of 109,864 results*