101 Chess Endgame Tips by Steve Giddins

By Steve Giddins

Popular chess writer Steve Giddins provides one hundred and one rules which are very important to profitable endgame play. via soaking up and figuring out those options and techniques, you'll make sure that you'll spot them after they are attainable on your personal video games. this is often an incredible ebook to learn with out utilizing a chess set, because the considerable diagrams consultant you thru the research and illustrate the most important issues. all kinds of endings are lined, together with either easy technical events and extra advanced strategic battles. the guidelines comprise either pithy principles of thumb and common considering equipment. The examples are drawn from a massive number of resources and in accordance with Giddins's reviews as a participant, trainer and pupil.

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Per presentarle descriviamo due possibili modi in cui puo` avvenire la preparazione preliminare di una partita. Immaginiamo che la scatola del gioco, appena acquistata, oppure dopo la fine di una partita, sia nella configurazione di base. Il giocatore che vuole giocare 1 Secondo la terminologia introdotta nel ‘primo piano’ sui grafi (Capitolo 5) questo grafo non e ` semplice, visto che ha ‘lati doppi’. Capitolo 7 ● Il Quindici: presentazione e prime domande 51 ha bisogno di rimescolare i blocchetti.

E` questo concetto astratto di grafo che vogliamo rendere preciso, senza riferirci a particolari concrete rappresentazioni grafiche che possono risultare ingannevoli come in Fig. 1. 1 Un grafo finito G e` una coppia ordinata di insiemi finiti (V , E) con una funzione t che associa ad ogni elemento e di E un sottoinsieme non vuoto t(e) ⊆ V con al pi`u due elementi. Chiamiamo V l’insieme dei vertici e E l’insieme degli archi di G. Per ogni arco e gli elementi di t(e) sono detti estremi di e. Due vertici u, v ∈ V sono detti adiacenti (o connessi da un arco) se {u, v} = t(e) per qualche arco e ∈ E.

Verifichiamo dunque l’identit`a del teorema: ∑ d(v) = n ⋅ (n − 1) = 2 ⋅ v∈V(K n ) n(n − 1) = 2∣E(K n )∣. 18 Un grafo G = (V , E) e` bipartito se e` possibile suddividere i suoi vertici in due insiemi disgiunti tali che ogni arco di G possieda un estremo in ognuno dei due insiemi. Ovvero, se esiste una partizione V = A ∪ B tale che, per ogni e ∈ E, t(e) ∩ A ≠ ∅ e t(e) ∩ B ≠ ∅. 16 segue facilmente dalla seguente uguaglianza: ∑ d(v) = ∑ d(v) = ∣E∣. v∈A v∈B Sapreste dimostrarla? 19 Dati due numeri naturali m e n, il grafo bipartito completo K m,n e` il grafo semplice su m + n vertici che possiede ‘il massimo numero di archi possibile’ (ecco perch´e si chiama ‘completo’) pur restando bipartito in due insiemi di vertici con m e n elementi, rispettivamente.

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