An even (respectively, odd) hole in a graph is an induced cycle with length that at least four. Bienstock proved detecting containing given vertex NP-complete. Conforti, Cornuéjols, Kapoor, and Vuškovi? gave the first known polynomial-time algorithm to determine whether contains holes. Chudnovsky, Kawarabayashi, Seymour estimated Conforti et al.'s runs O ( n 40 ) time on n-vertex reduced requir...

I n the June 2004 Security column (" A Patch in Nine Saves Time? " pp. 82-83), Bill Arbaugh makes two interesting observations: first, whoever has the tightest observe-orient-decide-act (OODA) loop will prevail in a confrontation; second, the infection rates of recent worms suggest that the good guys are losing the battle. Arbaugh offers some sensible suggestions to vendors and security profess...

due to the increasing cost and environmental impacts of fossil fuel consumption, using the renewable energies in data center has become an important and essential priority. although using renewable energies has less environmental harmful effects, but the high investment needed for their installations as well as their fluctuating power production characteristic, restricts their usage such that m...

In this discrete time process, guards are allowed to traverse edges of a network under the constraint that the neighbourhood of each vertex must be visited within a specified time interval t. Setting t = 0 the guards form a dominating set at all times. We show every rooted tree with relatively few leaves has a branch with a certain order and number of pendant vertices. This result is used to es...

The largest minimum weight of a self-dual doubly-even binary (n, k, d) code is d = 4bn/24c+ 4. Of such codes with length divisible by 24, the Golay Code is the only (24, 12, 8) code, the Extended Quadratic Residue Code is the only known (48, 24, 12) code, and there is no known (72, 36, 16) code. One may partition the search for a (48, 24, 12) self-dual doubly-even code into 3 cases. A previous ...

The notion of an extremal self-dual code has been introduced in 1 . As Gleason 2 remarks onemay use invariance properties of the weight enumerator of a self-dual code to deduce upper bounds on the minimum distance. Extremal codes are self-dual codes that achieve these bounds. The most wanted extremal code is a binary self-dual doubly even code of length 72 and minimum distance 16. One frequentl...